* fixed built version of semantics
authorjcheney@inf.ed.ac.uk
Mon, 25 Feb 2013 13:49:34 +0000
changeset 5734 8df8ca08c88d
parent 5733 413c06adfedb
child 5735 8c51d3082048
* fixed built version of semantics
semantics/prov-sem-review-20130226.html
--- a/semantics/prov-sem-review-20130226.html	Mon Feb 25 13:43:46 2013 +0000
+++ b/semantics/prov-sem-review-20130226.html	Mon Feb 25 13:49:34 2013 +0000
@@ -781,7 +781,7 @@
 #MathJax_Tooltip * {filter: none; opacity: 1; background: transparent}
 @font-face {font-family: MathJax_Blank; src: url('about:blank')}
 .MathJax .noError {vertical-align: ; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid}
-</style><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></head> 
+</style><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--><!--[if lt IE 9]><script src='http://www.w3.org/2008/site/js/html5shiv.js'></script><![endif]--></head> 
   <body><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>
     
@@ -834,7 +834,7 @@
     
   
   <hr>
-</div><div id="MathJax_Message" style="">Typesetting math: 51%</div> 
+</div><div id="MathJax_Message" style="display: none;"></div> 
 
     <section id="abstract" class="introductory"><h2>Abstract</h2>
 <p>
@@ -1718,48 +1718,47 @@
 <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" id="MathJax-Element-237-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4745"><span style="display: inline-block; position: relative; width: 213px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4746"><span class="mi" id="MathJax-Span-4747" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4748" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4749" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-4750" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-4751" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4752" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4753" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4754" 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-4755" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4756" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4757" 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-4758" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4759" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4760" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4761" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4762" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4763" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4764" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4765" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4766" 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-4767" 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-4768" 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-4769" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4770" 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-237">W,\rho \models used(id,a,e,t,attrs)</script> holds if and only if:</p>
 
-<li>[WF] The identifier <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-238-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4771"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4772"><span class="mi" id="MathJax-Span-4773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4774" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-238">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-239-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4775"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4776"><span class="mi" id="MathJax-Span-4777" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4778" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4779" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4780" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4781" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4782" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4783" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4784" 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-4785" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4786" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4787" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4788" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4790" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4791" 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-4792" style="font-family: STIXGeneral-Italic;">s</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-239">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-240-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4793"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4794"><span class="mi" id="MathJax-Span-4795" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-240">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(id) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-241-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4796"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4797"><span class="mi" id="MathJax-Span-4798" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4799" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4801" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4802" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4803" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4804" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4805" 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-4806" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-4809" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4810" 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-4811" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4812" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4813" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4814" 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-4815" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4816" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4817" style="font-family: STIXGeneral-Italic;">s</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-241">act = \rho(id) \in Activities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-242-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4818"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4819"><span class="mi" id="MathJax-Span-4820" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-242">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-243-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4821"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4822"><span class="mi" id="MathJax-Span-4823" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4825" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4826" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4827" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4829" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4830" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4833" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4834" 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-4835" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4836" 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-4837" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4838" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4839" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-238-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4771"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4772"><span class="mi" id="MathJax-Span-4773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4774" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-238">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-239-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4775"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4776"><span class="mi" id="MathJax-Span-4777" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4778" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4779" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4780" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4781" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4782" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4783" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4784" 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-4785" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4786" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4787" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4788" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4790" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4791" 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-4792" style="font-family: STIXGeneral-Italic;">s</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-239">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-244-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4840"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4841"><span class="mi" id="MathJax-Span-4842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4843" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-244">evt</script> is part of <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processed" id="MathJax-Element-245-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4845"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4846"><span class="mi" id="MathJax-Span-4847" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4848" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4849" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-245">act</script>, i.e. <span class="MathJax_Preview">(evt,act) \in EventActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-246-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4850"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4851"><span class="mo" id="MathJax-Span-4852" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4854" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4856" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4857" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4858" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4859" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4860" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4861" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4862" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4863" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4865" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4866" 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-4867" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-4868" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4869" 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-4870" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4871" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4872" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4873" 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-4874" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4875" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4876" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-246">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-247-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4877"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4878"><span class="mi" id="MathJax-Span-4879" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4880" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4881" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-247">evt</script> is <span class="MathJax_Preview">use</span><span class="MathJax MathJax_Processed" id="MathJax-Element-248-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4882"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4883"><span class="mi" id="MathJax-Span-4884" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-4885" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4886" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-248">use</script>, i.e., <span class="MathJax_Preview">type(evt) = use</span><span class="MathJax MathJax_Processed" id="MathJax-Element-249-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4887"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4888"><span class="mi" id="MathJax-Span-4889" 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-4890" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-4891" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-4892" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4893" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4895" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4896" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4897" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4898" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4899" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4900" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4901" style="font-family: STIXGeneral-Italic;">e</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: -5px;"></span></span></nobr></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" id="MathJax-Element-240-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4793"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4794"><span class="mi" id="MathJax-Span-4795" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-240">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-241-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4796"><span style="display: inline-block; position: relative; width: 178px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4797"><span class="mi" id="MathJax-Span-4798" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4799" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4801" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4802" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4803" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4804" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4805" 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-4806" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-4809" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4810" 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-4811" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4812" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4813" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4814" 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-4815" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4816" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4817" style="font-family: STIXGeneral-Italic;">s</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-241">act = \rho(id) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-250-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4902"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4903"><span class="mi" id="MathJax-Span-4904" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4905" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-250">evt</script> occurred at time <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-251-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4907"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4908"><span class="mi" id="MathJax-Span-4909" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-251">t</script>, i.e. <span class="MathJax_Preview">time(evt) = t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-252-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4910"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4911"><span class="mi" id="MathJax-Span-4912" 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-4913" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4914" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4915" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4916" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4917" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4918" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4919" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4920" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4921" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4922" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-242-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4818"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4819"><span class="mi" id="MathJax-Span-4820" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-242">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-243-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4821"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4822"><span class="mi" id="MathJax-Span-4823" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4824" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4825" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4826" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4827" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-4828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4829" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4830" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4833" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4834" 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-4835" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4836" 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-4837" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4838" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4839" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-243">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-253-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4923"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4924"><span class="mi" id="MathJax-Span-4925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4926" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4927" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-253">evt</script> used <span class="MathJax_Preview">obj</span><span class="MathJax MathJax_Processed" id="MathJax-Element-254-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4928"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4929"><span class="mi" id="MathJax-Span-4930" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-4931" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-4932" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></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-254">obj</script>, i.e. <span class="MathJax_Preview">(evt,ent) \in Used</span><span class="MathJax MathJax_Processed" id="MathJax-Element-255-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4933"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4934"><span class="mo" id="MathJax-Span-4935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4936" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4937" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4939" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4940" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4941" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4942" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4943" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4944" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4945" style="font-family: STIXGeneral-Italic; padding-left: 6px;">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-4946" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4947" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4948" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-244-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4840"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4841"><span class="mi" id="MathJax-Span-4842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4843" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4844" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-244">evt</script> is part of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-245-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4845"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4846"><span class="mi" id="MathJax-Span-4847" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4848" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4849" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-245">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-246-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4850"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4851"><span class="mo" id="MathJax-Span-4852" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4854" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4855" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4856" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4857" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4858" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4859" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4860" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4861" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4862" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-4863" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4864" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4865" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4866" 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-4867" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-4868" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4869" 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-4870" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4871" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4872" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4873" 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-4874" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4875" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4876" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-246">(evt,act) \in EventActivities</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-256-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4949"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4950"><span class="mi" id="MathJax-Span-4951" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4952" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4953" 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-4954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4955" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-4956" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4957" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4958" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4959" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4960" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4961" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4962" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4963" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4964" 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-4965" 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-4966" 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-4967" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4968" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-247-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4877"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4878"><span class="mi" id="MathJax-Span-4879" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4880" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4881" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-247">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-248-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4882"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4883"><span class="mi" id="MathJax-Span-4884" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-4885" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4886" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-248">use</script>, i.e., <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-249-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4887"><span style="display: inline-block; position: relative; width: 115px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4888"><span class="mi" id="MathJax-Span-4889" 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-4890" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-4891" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-4892" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4893" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4894" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4895" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4896" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4897" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4898" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4899" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-4900" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4901" style="font-family: STIXGeneral-Italic;">e</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-249">type(evt) = use</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-250-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4902"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4903"><span class="mi" id="MathJax-Span-4904" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4905" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4906" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-250">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-251-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4907"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4908"><span class="mi" id="MathJax-Span-4909" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-251">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-252-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4910"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4911"><span class="mi" id="MathJax-Span-4912" 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-4913" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4914" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4915" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-4916" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4917" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4918" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4919" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4920" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4921" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-4922" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-252">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-253-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4923"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4924"><span class="mi" id="MathJax-Span-4925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4926" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4927" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-253">evt</script> used <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-254-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4928"><span style="display: inline-block; position: relative; width: 25px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4929"><span class="mi" id="MathJax-Span-4930" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-4931" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-4932" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></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-254">obj</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-255-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4933"><span style="display: inline-block; position: relative; width: 128px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4934"><span class="mo" id="MathJax-Span-4935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4936" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4937" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4938" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4939" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4940" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4941" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4942" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4943" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-4944" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-4945" style="font-family: STIXGeneral-Italic; padding-left: 6px;">U<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-4946" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4947" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4948" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-255">(evt,ent) \in Used</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-256-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4949"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4950"><span class="mi" id="MathJax-Span-4951" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-4952" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4953" 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-4954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-4955" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-4956" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4957" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-4958" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4959" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-4960" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4961" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4962" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4963" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4964" 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-4965" 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-4966" 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-4967" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-4968" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-256">match(W,evt,attrs)</script>.
 </li></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">wasInvalidatedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-257-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4969"><span style="display: inline-block; position: relative; width: 258px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4970"><span class="mi" id="MathJax-Span-4971" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-4972" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4973" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4974" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-4975" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4976" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4977" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4978" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-4979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4980" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4981" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4982" 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-4983" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4984" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4985" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-4986" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-4987" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4988" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4989" 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-4990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4992" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4993" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4994" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4995" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4996" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4997" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4998" 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-4999" 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-5000" 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-5001" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5002" 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-257">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-258-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5003"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5004"><span class="mi" id="MathJax-Span-5005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5006" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-258">id</script> is an event identifier, <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-259-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5007"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5008"><span class="mi" id="MathJax-Span-5009" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-259">e</script> is an entity identifier, <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-260-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5010"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5011"><span class="mi" id="MathJax-Span-5012" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-260">a</script> is an activity identifier, <span class="MathJax_Preview">attrs</span><span class="MathJax MathJax_Processed" id="MathJax-Element-261-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5013"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5014"><span class="mi" id="MathJax-Span-5015" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5016" 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-5017" 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-5018" 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-5019" style="font-family: STIXGeneral-Italic;">s</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: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-261">attrs</script> is a set of attribute-value pairs, and <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-262-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5020"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5021"><span class="mi" id="MathJax-Span-5022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></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">W,\rho \models
-  wasInvalidatedBy(id,e,a,t,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-263-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5023"><span style="display: inline-block; position: relative; width: 317px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5024"><span class="mi" id="MathJax-Span-5025" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5026" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5027" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5028" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5029" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5030" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5032" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5033" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5034" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5036" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5037" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5038" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5039" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5040" 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-5041" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5042" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5043" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5044" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5045" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5046" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5047" 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-5048" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5049" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5050" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5051" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5052" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5053" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5054" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5055" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5056" 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-5057" 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-5058" 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-5059" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5060" 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-263">W,\rho \models
+<p>The invalidation formula is of the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-257-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-4969"><span style="display: inline-block; position: relative; width: 258px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-4970"><span class="mi" id="MathJax-Span-4971" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-4972" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4973" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-4974" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-4975" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-4976" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-4977" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4978" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-4979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4980" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4981" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-4982" 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-4983" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-4984" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-4985" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-4986" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-4987" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-4988" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-4989" 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-4990" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4991" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-4992" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4993" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-4994" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4995" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-4996" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-4997" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-4998" 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-4999" 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-5000" 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-5001" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5002" 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-257">wasInvalidatedBy(id,e,a,t,attrs)</script> where <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-258-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5003"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5004"><span class="mi" id="MathJax-Span-5005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5006" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-258">id</script> is an event identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-259-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5007"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5008"><span class="mi" id="MathJax-Span-5009" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-259">e</script> is an entity identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-260-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5010"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5011"><span class="mi" id="MathJax-Span-5012" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-260">a</script> is an activity identifier, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-261-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5013"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5014"><span class="mi" id="MathJax-Span-5015" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5016" 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-5017" 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-5018" 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-5019" style="font-family: STIXGeneral-Italic;">s</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: 12.8px; vertical-align: -1.3px;"></span></span></nobr></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" id="MathJax-Element-262-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5020"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5021"><span class="mi" id="MathJax-Span-5022" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></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" id="MathJax-Element-263-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5023"><span style="display: inline-block; position: relative; width: 317px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5024"><span class="mi" id="MathJax-Span-5025" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5026" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5027" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5028" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5029" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5030" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5031" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5032" style="font-family: STIXGeneral-Italic;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5033" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5034" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5036" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5037" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5038" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5039" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5040" 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-5041" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5042" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5043" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5044" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5045" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5046" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5047" 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-5048" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5049" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5050" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5051" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5052" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5053" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5054" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5055" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5056" 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-5057" 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-5058" 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-5059" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5060" 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-263">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">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-264-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5061"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5062"><span class="mi" id="MathJax-Span-5063" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5064" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-264">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-265-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5065"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5066"><span class="mi" id="MathJax-Span-5067" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5068" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5069" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5070" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5071" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5072" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5073" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5074" 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-5075" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5076" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5077" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5078" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5080" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5081" 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-5082" style="font-family: STIXGeneral-Italic;">s</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-265">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-266-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5083"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5084"><span class="mi" id="MathJax-Span-5085" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-266">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-267-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5086"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5087"><span class="mi" id="MathJax-Span-5088" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5089" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5091" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5092" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5093" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5094" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5095" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5096" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5097" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5098" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5099" 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-5100" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5101" 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-5102" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5103" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5104" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-267">ent = \rho(e) \in Entities</script>.
-</li>
-<li>[WF] The identifier <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-268-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5105"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5106"><span class="mi" id="MathJax-Span-5107" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-268">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-269-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5108"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5109"><span class="mi" id="MathJax-Span-5110" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5111" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5112" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5113" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5114" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5116" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5117" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5118" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5119" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5120" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5121" 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-5122" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5123" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5124" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5125" 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-5126" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5127" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5128" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-264-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5061"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5062"><span class="mi" id="MathJax-Span-5063" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5064" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-264">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-265-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5065"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5066"><span class="mi" id="MathJax-Span-5067" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5068" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5069" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5070" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5071" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5072" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5073" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5074" 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-5075" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5076" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5077" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5078" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5080" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5081" 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-5082" style="font-family: STIXGeneral-Italic;">s</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-265">evt = \rho(id) \in Events</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-270-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5129"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5130"><span class="mi" id="MathJax-Span-5131" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5132" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5133" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-270">evt</script> is involved in <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processed" id="MathJax-Element-271-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5134"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5135"><span class="mi" id="MathJax-Span-5136" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5137" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5138" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-271">act</script>, that is, <span class="MathJax_Preview">(evt,act) \in EventActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-272-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5139"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5140"><span class="mo" id="MathJax-Span-5141" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5143" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5144" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5145" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5146" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5147" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5149" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5150" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5151" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5154" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5155" 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-5156" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5157" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5158" 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-5159" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5160" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5161" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5162" 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-5163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5164" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5165" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-272">(evt,act) \in EventActivities</script>.
-</li>
-<li>The type of <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-273-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5166"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5167"><span class="mi" id="MathJax-Span-5168" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5169" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-273">evt</script> is <span class="MathJax_Preview">invalidation</span><span class="MathJax MathJax_Processed" id="MathJax-Element-274-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5171"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5172"><span class="mi" id="MathJax-Span-5173" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5174" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5175" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5176" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5177" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5178" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5179" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5180" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5181" 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-5182" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5183" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5184" style="font-family: STIXGeneral-Italic;">n</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: 15.6px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-274">invalidation</script>, i.e. <span class="MathJax_Preview">type(evt) = invalidation</span><span class="MathJax MathJax_Processed" id="MathJax-Element-275-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5185"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5186"><span class="mi" id="MathJax-Span-5187" 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-5188" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5189" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5190" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5191" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5192" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5193" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5194" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5195" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5196" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5197" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-5198" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5199" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5200" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5201" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5202" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5203" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5204" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5205" 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-5206" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5207" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5208" style="font-family: STIXGeneral-Italic;">n</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-275">type(evt) = invalidation</script>.
+<li>[WF] The identifier <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-266-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5083"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5084"><span class="mi" id="MathJax-Span-5085" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-266">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-267-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5086"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5087"><span class="mi" id="MathJax-Span-5088" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5089" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5090" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5091" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5092" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5093" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5094" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5095" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5096" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5097" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5098" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5099" 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-5100" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5101" 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-5102" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5103" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5104" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-267">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-276-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5209"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5210"><span class="mi" id="MathJax-Span-5211" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5212" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-276">evt</script> occurred at time <span class="MathJax_Preview">t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-277-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5214"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5215"><span class="mi" id="MathJax-Span-5216" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-277">t</script>, i.e. <span class="MathJax_Preview">time(evt) = t</span><span class="MathJax MathJax_Processed" id="MathJax-Element-278-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5217"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5218"><span class="mi" id="MathJax-Span-5219" 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-5220" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5221" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5222" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5223" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5224" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5225" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5226" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5227" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5228" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5229" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-268-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5105"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5106"><span class="mi" id="MathJax-Span-5107" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-268">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-269-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5108"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5109"><span class="mi" id="MathJax-Span-5110" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5111" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5112" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5113" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5114" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5116" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5117" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5118" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5119" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5120" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5121" 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-5122" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5123" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5124" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5125" 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-5126" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5127" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5128" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-269">act = \rho(a) \in Activities</script>.
 </li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-279-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5230"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5231"><span class="mi" id="MathJax-Span-5232" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5233" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-279">evt</script> invalidated <span class="MathJax_Preview">ent</span><span class="MathJax MathJax_Processed" id="MathJax-Element-280-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5235"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5236"><span class="mi" id="MathJax-Span-5237" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5238" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5239" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-280">ent</script>, i.e. <span class="MathJax_Preview">(evt,ent) \in Invalidated</span><span class="MathJax MathJax_Processed" id="MathJax-Element-281-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5240"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5241"><span class="mo" id="MathJax-Span-5242" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5243" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5244" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5245" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5248" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5250" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5251" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5252" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5253" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5254" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5255" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5256" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5257" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5258" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5259" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5260" 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-5261" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5262" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-270-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5129"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5130"><span class="mi" id="MathJax-Span-5131" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5132" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5133" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-270">evt</script> is involved in <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-271-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5134"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5135"><span class="mi" id="MathJax-Span-5136" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5137" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5138" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-271">act</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-272-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5139"><span style="display: inline-block; position: relative; width: 200px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5140"><span class="mo" id="MathJax-Span-5141" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5142" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5143" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5144" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5145" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5146" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5147" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5148" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5149" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5150" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5151" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5154" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5155" 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-5156" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5157" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5158" 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-5159" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5160" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5161" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5162" 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-5163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5164" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5165" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-272">(evt,act) \in EventActivities</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-282-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5263"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5264"><span class="mi" id="MathJax-Span-5265" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5266" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5267" 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-5268" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5269" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5270" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5271" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5272" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5273" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5274" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5275" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5276" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5277" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5278" 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-5279" 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-5280" 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-5281" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5282" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-273-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5166"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5167"><span class="mi" id="MathJax-Span-5168" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5169" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5170" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-273">evt</script> is <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-274-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5171"><span style="display: inline-block; position: relative; width: 94px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5172"><span class="mi" id="MathJax-Span-5173" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5174" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5175" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5176" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5177" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5178" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5179" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5180" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5181" 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-5182" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5183" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5184" style="font-family: STIXGeneral-Italic;">n</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: 15.6px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-274">invalidation</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-275-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5185"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5186"><span class="mi" id="MathJax-Span-5187" 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-5188" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5189" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5190" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5191" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5192" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5193" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5194" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5195" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5196" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5197" style="font-family: STIXGeneral-Italic; padding-left: 6px;">i</span><span class="mi" id="MathJax-Span-5198" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5199" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5200" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5201" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5202" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5203" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5204" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5205" 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-5206" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5207" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5208" style="font-family: STIXGeneral-Italic;">n</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-275">type(evt) = invalidation</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-276-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5209"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5210"><span class="mi" id="MathJax-Span-5211" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5212" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5213" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-276">evt</script> occurred at time <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-277-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5214"><span style="display: inline-block; position: relative; width: 6px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5215"><span class="mi" id="MathJax-Span-5216" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-277">t</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-278-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5217"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5218"><span class="mi" id="MathJax-Span-5219" 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-5220" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5221" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5222" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5223" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5224" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5225" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5226" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5227" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5228" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5229" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-278">time(evt) = t</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-279-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5230"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5231"><span class="mi" id="MathJax-Span-5232" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5233" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5234" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-279">evt</script> invalidated <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-280-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5235"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5236"><span class="mi" id="MathJax-Span-5237" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5238" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5239" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-280">ent</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-281-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5240"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5241"><span class="mo" id="MathJax-Span-5242" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5243" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5244" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5245" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5246" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5247" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5248" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5249" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5250" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5251" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5252" style="font-family: STIXGeneral-Italic; padding-left: 6px;">I<span style="display: inline-block; overflow: hidden; height: 1px; width: 1px;"></span></span><span class="mi" id="MathJax-Span-5253" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5254" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5255" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5256" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5257" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5258" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5259" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5260" 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-5261" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5262" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-281">(evt,ent) \in Invalidated</script>.
+</li>
+<li>The attribute values match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-282-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5263"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5264"><span class="mi" id="MathJax-Span-5265" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5266" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5267" 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-5268" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5269" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5270" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5271" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5272" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5273" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5274" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5275" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5276" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5277" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5278" 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-5279" 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-5280" 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-5281" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5282" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-282">match(W,evt,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1767,77 +1766,74 @@
 
 <h4><span class="secno">4.4.4 </span> Association </h4>
 
-<p>An association formula has the form <span class="MathJax_Preview">wasAssociatedWith(id,a,ag,pl,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-283-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5283"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5284"><span class="mi" id="MathJax-Span-5285" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5286" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5287" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5288" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5290" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5291" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5292" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5294" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5295" 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-5296" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5297" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5298" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5299" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5300" 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-5301" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5302" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5304" 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-5305" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5306" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5309" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5310" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5311" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5312" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5313" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5314" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5315" 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-5316" 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-5317" 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-5318" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5319" 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-283">wasAssociatedWith(id,a,ag,pl,attrs)</script>.</p>
+<p>An association formula has the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-283-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5283"><span style="display: inline-block; position: relative; width: 290px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5284"><span class="mi" id="MathJax-Span-5285" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5286" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5287" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5288" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5289" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5290" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5291" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5292" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5294" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5295" 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-5296" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5297" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5298" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5299" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5300" 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-5301" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5302" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5304" 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-5305" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5306" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5307" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5308" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5309" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5310" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5311" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5312" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5313" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5314" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5315" 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-5316" 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-5317" 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-5318" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5319" 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-283">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">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-284-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5320"><span style="display: inline-block; position: relative; width: 350px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5321"><span class="mi" id="MathJax-Span-5322" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5323" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5324" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5325" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5326" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5327" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5328" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5329" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5330" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5331" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5332" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5333" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5334" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5335" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5336" 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-5337" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5338" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5339" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5340" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5341" 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-5342" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5343" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5344" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5345" 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-5346" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5347" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5348" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5349" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5350" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5351" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5352" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5354" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5355" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5356" 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-5357" 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-5358" 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-5359" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5360" 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-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" id="MathJax-Element-284-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5320"><span style="display: inline-block; position: relative; width: 350px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5321"><span class="mi" id="MathJax-Span-5322" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5323" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5324" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5325" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5326" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5327" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5328" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5329" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5330" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5331" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5332" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5333" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5334" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5335" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5336" 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-5337" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5338" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5339" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5340" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5341" 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-5342" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5343" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5344" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5345" 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-5346" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5347" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-5348" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5349" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5350" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5351" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5352" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5353" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5354" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5355" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5356" 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-5357" 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-5358" 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-5359" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5360" 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-284">W,\rho \models wasAssociatedWith(id,a,ag,pl,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">assoc</span><span class="MathJax MathJax_Processed" id="MathJax-Element-285-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5361"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5362"><span class="mi" id="MathJax-Span-5363" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5364" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5365" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5366" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5367" style="font-family: STIXGeneral-Italic;">c</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: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-285">assoc</script> denotes an association <span class="MathJax_Preview">assoc = \rho(id) \in Associations</span><span class="MathJax MathJax_Processed" id="MathJax-Element-286-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5368"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5369"><span class="mi" id="MathJax-Span-5370" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5371" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5372" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5373" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5374" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5375" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5376" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5377" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5378" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5379" 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-5380" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5381" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5382" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5383" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5384" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5385" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5386" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5387" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5388" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5389" 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-5390" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5391" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5392" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5393" style="font-family: STIXGeneral-Italic;">s</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-286">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processed" id="MathJax-Element-287-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5394"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5395"><span class="mi" id="MathJax-Span-5396" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-287">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-288-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5397"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5398"><span class="mi" id="MathJax-Span-5399" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5400" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5401" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5402" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5403" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5404" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5405" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5406" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5407" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5408" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5409" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5410" 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-5411" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5412" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5413" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5414" 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-5415" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5416" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5417" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-285-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5361"><span style="display: inline-block; position: relative; width: 42px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5362"><span class="mi" id="MathJax-Span-5363" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5364" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5365" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5366" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5367" style="font-family: STIXGeneral-Italic;">c</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: 10.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-285">assoc</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-286-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5368"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5369"><span class="mi" id="MathJax-Span-5370" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5371" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5372" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5373" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5374" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5375" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5376" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5377" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5378" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5379" 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-5380" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5381" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5382" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5383" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5384" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5385" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5386" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5387" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5388" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5389" 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-5390" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5391" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5392" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5393" style="font-family: STIXGeneral-Italic;">s</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-286">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag</span><span class="MathJax MathJax_Processed" id="MathJax-Element-289-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5418"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5419"><span class="mi" id="MathJax-Span-5420" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5421" style="font-family: STIXGeneral-Italic;">g</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: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-289">ag</script> denotes an agent <span class="MathJax_Preview">agent = \rho(ag) \in Agents</span><span class="MathJax MathJax_Processed" id="MathJax-Element-290-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5422"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5423"><span class="mi" id="MathJax-Span-5424" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5425" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5426" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5427" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5429" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5430" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5431" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5432" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5433" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5437" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5438" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5439" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5440" 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-5441" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-287-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5394"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5395"><span class="mi" id="MathJax-Span-5396" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-287">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-288-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5397"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5398"><span class="mi" id="MathJax-Span-5399" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5400" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5401" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5402" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5403" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5404" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5405" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-5406" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5407" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5408" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5409" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5410" 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-5411" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5412" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5413" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5414" 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-5415" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5416" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5417" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-288">act = \rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">pl</span><span class="MathJax MathJax_Processed" id="MathJax-Element-291-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5442"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5443"><span class="mi" id="MathJax-Span-5444" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5445" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></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-291">pl</script> is either the placeholder <span class="MathJax_Preview">-</span><span class="MathJax MathJax_Processed" id="MathJax-Element-292-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5446"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5447"><span class="mo" id="MathJax-Span-5448" 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: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-292">-</script> or denotes a plan <span class="MathJax_Preview">plan=\rho(pl) \in Plans</span><span class="MathJax MathJax_Processed" id="MathJax-Element-293-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5449"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5450"><span class="mi" id="MathJax-Span-5451" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5452" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5453" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5454" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5455" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5456" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5457" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5458" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5459" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5460" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5461" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5462" style="font-family: STIXGeneral-Italic; padding-left: 6px;">P</span><span class="mi" id="MathJax-Span-5463" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5464" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5465" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5466" style="font-family: STIXGeneral-Italic;">s</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-293">plan=\rho(pl) \in Plans</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-289-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5418"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5419"><span class="mi" id="MathJax-Span-5420" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5421" style="font-family: STIXGeneral-Italic;">g</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: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-289">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-290-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5422"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5423"><span class="mi" id="MathJax-Span-5424" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5425" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5426" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5427" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5428" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5429" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5430" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5431" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5432" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5433" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-5434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5437" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5438" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5439" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5440" 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-5441" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-290">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The association associates the agent with the activity and plan, i.e. <span class="MathJax_Preview">(assoc,agent,act,plan) \in AssociatedWith</span><span class="MathJax MathJax_Processed" id="MathJax-Element-294-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5467"><span style="display: inline-block; position: relative; width: 324px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5468"><span class="mo" id="MathJax-Span-5469" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5470" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5471" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5472" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5473" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5474" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5475" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5476" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5477" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5478" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5479" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5480" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5483" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5485" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5486" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5487" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5488" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5489" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5490" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5491" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5492" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5493" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5494" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5495" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5496" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5497" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5498" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5499" 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-5500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5501" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5502" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5504" 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-5505" style="font-family: STIXGeneral-Italic;">h</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-294">(assoc,agent,act,plan) \in AssociatedWith</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-291-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5442"><span style="display: inline-block; position: relative; width: 15px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5443"><span class="mi" id="MathJax-Span-5444" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5445" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></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-291">pl</script> is either the placeholder <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-292-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5446"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(39.5px 19360px 48.7px -7.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5447"><span class="mo" id="MathJax-Span-5448" 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: 5.2px; vertical-align: 1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-292">-</script> or denotes a plan <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-293-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5449"><span style="display: inline-block; position: relative; width: 164px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -10.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5450"><span class="mi" id="MathJax-Span-5451" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5452" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5453" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5454" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5455" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5456" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5457" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5458" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5459" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mo" id="MathJax-Span-5460" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5461" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5462" style="font-family: STIXGeneral-Italic; padding-left: 6px;">P</span><span class="mi" id="MathJax-Span-5463" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5464" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5465" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5466" style="font-family: STIXGeneral-Italic;">s</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-293">plan=\rho(pl) \in Plans</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,assoc,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-295-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5506"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5507"><span class="mi" id="MathJax-Span-5508" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5509" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5510" 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-5511" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5512" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5513" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5514" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5515" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5516" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5517" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5518" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5519" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5520" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5521" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5522" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5523" 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-5524" 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-5525" 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-5526" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5527" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-294-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5467"><span style="display: inline-block; position: relative; width: 324px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5468"><span class="mo" id="MathJax-Span-5469" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5470" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5471" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5472" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5473" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5474" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5475" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5476" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5477" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-5478" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5479" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5480" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5481" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5482" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5483" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5484" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5485" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5486" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">p</span><span class="mi" id="MathJax-Span-5487" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5488" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5489" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5490" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5491" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5492" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5493" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5494" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5495" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5496" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5497" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5498" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5499" 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-5500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5501" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5502" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mi" id="MathJax-Span-5503" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5504" 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-5505" style="font-family: STIXGeneral-Italic;">h</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-294">(assoc,agent,act,plan) \in AssociatedWith</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-295-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5506"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5507"><span class="mi" id="MathJax-Span-5508" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5509" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5510" 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-5511" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5512" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5513" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5514" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5515" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5516" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5517" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5518" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5519" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-5520" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-5521" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5522" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5523" 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-5524" 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-5525" 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-5526" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5527" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-295">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">wasStartedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-296-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5528"><span style="display: inline-block; position: relative; width: 247px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5529"><span class="mi" id="MathJax-Span-5530" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5531" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5532" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5533" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5534" 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-5535" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5536" 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-5537" 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-5538" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5539" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5540" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5541" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5542" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5543" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5544" 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-5545" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5546" 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-5547" 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-5548" 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-5549" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5550" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5551" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5552" 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-5553" 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-5554" 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-5555" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5556" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5557" 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-5558" 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-5559" 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-5560" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5561" 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-296">wasStartedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+<p>A start formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-296-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5528"><span style="display: inline-block; position: relative; width: 247px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5529"><span class="mi" id="MathJax-Span-5530" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5531" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5532" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5533" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5534" 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-5535" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5536" 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-5537" 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-5538" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5539" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5540" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5541" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5542" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5543" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5544" 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-5545" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5546" 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-5547" 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-5548" 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-5549" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5550" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5551" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5552" 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-5553" 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-5554" 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-5555" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5556" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5557" 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-5558" 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-5559" 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-5560" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5561" 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-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">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-297-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5562"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5563"><span class="mi" id="MathJax-Span-5564" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5565" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5566" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5567" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5568" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5569" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5570" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5571" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5572" 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-5573" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5574" 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-5575" 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-5576" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5577" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5578" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5579" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5580" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5581" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5582" 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-5583" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5584" 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-5585" 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-5586" 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-5587" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5588" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5589" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5590" 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-5591" 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-5592" 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-5593" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5594" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5595" 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-5596" 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-5597" 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-5598" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5599" 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-297">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-297-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5562"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5563"><span class="mi" id="MathJax-Span-5564" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5565" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5566" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5567" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5568" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5569" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5570" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5571" style="font-family: STIXGeneral-Italic;">S<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.2px;"></span></span><span class="mi" id="MathJax-Span-5572" 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-5573" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5574" 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-5575" 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-5576" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5577" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5578" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5579" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5580" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5581" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5582" 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-5583" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5584" 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-5585" 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-5586" 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-5587" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5588" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5589" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5590" 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-5591" 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-5592" 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-5593" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5594" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5595" 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-5596" 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-5597" 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-5598" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5599" 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-297">W,\rho \models wasStartedBy(id,a_2,e,a_1,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-298-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5600"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5601"><span class="mi" id="MathJax-Span-5602" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5603" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-298">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-299-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5604"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5605"><span class="mi" id="MathJax-Span-5606" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5607" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5609" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5610" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5611" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5612" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5613" 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-5614" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5615" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5616" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5617" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5618" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5619" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5620" 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-5621" style="font-family: STIXGeneral-Italic;">s</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-299">evt = \rho(id) \in Events</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">a_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-300-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5622"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5623"><span class="msubsup" id="MathJax-Span-5624"><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-5625" 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-5626" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-300">a_2</script> denotes an activity <span class="MathJax_Preview">act_2 = \rho(a_2) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-301-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5627"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5628"><span class="mi" id="MathJax-Span-5629" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5630" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5631"><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-5632" 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-5633" 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-5634" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5635" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5636" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5637"><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-5638" 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-5639" 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-5640" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5641" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5642" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5643" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5644" 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-5645" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5646" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5647" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5648" 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-5649" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5651" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-301">act_2 = \rho(a_2) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-302-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5652"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5653"><span class="mi" id="MathJax-Span-5654" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-302">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-303-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5655"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5656"><span class="mi" id="MathJax-Span-5657" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5658" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5660" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5661" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5662" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5663" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5664" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5665" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5666" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5667" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5668" 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-5669" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5670" 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-5671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5672" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5673" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-303">ent = \rho(e) \in Entities</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-298-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5600"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5601"><span class="mi" id="MathJax-Span-5602" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5603" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-298">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-299-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5604"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5605"><span class="mi" id="MathJax-Span-5606" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5607" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5608" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5609" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5610" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5611" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5612" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5613" 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-5614" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5615" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5616" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5617" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5618" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5619" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5620" 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-5621" style="font-family: STIXGeneral-Italic;">s</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-299">evt = \rho(id) \in Events</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-304-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5674"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5675"><span class="msubsup" id="MathJax-Span-5676"><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-5677" 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-5678" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-304">a_1</script> denotes an activity <span class="MathJax_Preview">act_1 = \rho(a_1) \in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-305-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5679"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5680"><span class="mi" id="MathJax-Span-5681" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5682" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5683"><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-5684" 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-5685" 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-5686" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5687" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5688" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5689"><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-5690" 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-5691" 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-5692" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5693" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5694" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5695" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5696" 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-5697" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5698" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5699" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5700" 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-5701" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5702" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5703" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-305">act_1 = \rho(a_1) \in Activities</script>.
-</li>
-<li>The event <span class="MathJax_Preview">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-306-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5704"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5705"><span class="mi" id="MathJax-Span-5706" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5707" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-306">evt</script> has type <span class="MathJax_Preview">start</span><span class="MathJax MathJax_Processed" id="MathJax-Element-307-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5709"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5710"><span class="mi" id="MathJax-Span-5711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5712" 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-5713" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5714" 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-5715" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-307">start</script>, i.e. <span class="MathJax_Preview">type(evt) = start</span><span class="MathJax MathJax_Processed" id="MathJax-Element-308-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5716"><span style="display: inline-block; position: relative; width: 125px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5717"><span class="mi" id="MathJax-Span-5718" 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-5719" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5720" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5721" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5722" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5723" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5724" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5725" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5726" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5727" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5728" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-5729" 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-5730" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5731" 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-5732" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-308">type(evt) = start</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-300-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5622"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5623"><span class="msubsup" id="MathJax-Span-5624"><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-5625" 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-5626" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-300">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-301-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5627"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5628"><span class="mi" id="MathJax-Span-5629" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5630" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5631"><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-5632" 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-5633" 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-5634" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5635" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5636" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5637"><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-5638" 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-5639" 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-5640" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5641" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5642" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5643" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5644" 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-5645" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5646" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5647" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5648" 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-5649" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5650" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5651" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-301">act_2 = \rho(a_2) \in Activities</script>.
 </li>
-<li>The event happened at the start of <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-309-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5733"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5734"><span class="mi" id="MathJax-Span-5735" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5736" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5737"><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-5738" 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-5739" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-309">act_2</script>, that is, <span class="MathJax_Preview">(evt,act_2)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-310-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5740"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5741"><span class="mo" id="MathJax-Span-5742" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5743" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5744" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5748" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5749"><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-5750" 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-5751" 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-5752" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5753" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5754" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5755" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5757" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5758" 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-5759" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5760" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5761" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5762" 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-5763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5764" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5765" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5766" 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-5767" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5769" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-310">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview">min(lifetime(act_2)) = time(evt)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-311-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5770"><span style="display: inline-block; position: relative; width: 234px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5771"><span class="mi" id="MathJax-Span-5772" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5774" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5775" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5776" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5777" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5778" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-5779" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5780" 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-5781" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5782" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5783" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5784" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5785" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5786" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5787"><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-5788" 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-5789" 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-5790" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5791" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5792" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5793" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5795" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5796" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5797" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5798" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5799" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5801" 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-311">min(lifetime(act_2)) = time(evt)</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-302-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5652"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5653"><span class="mi" id="MathJax-Span-5654" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-302">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-303-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5655"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5656"><span class="mi" id="MathJax-Span-5657" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5658" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5659" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5660" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5661" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5662" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5663" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5664" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5665" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5666" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5667" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5668" 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-5669" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5670" 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-5671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5672" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5673" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-303">ent = \rho(e) \in Entities</script>.
 </li>
-<li>TODO: The entity <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-312-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5802"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5803"><span class="mi" id="MathJax-Span-5804" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-312">e</script> was generated by <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-313-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5805"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5806"><span class="mi" id="MathJax-Span-5807" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5808" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5809"><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-5810" 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-5811" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-313">act_1</script> and started <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-314-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5812"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5813"><span class="mi" id="MathJax-Span-5814" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5815" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5816"><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-5817" 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-5818" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-314">act_2</script>.
-</li><li>The event happened during <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-315-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5819"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5820"><span class="mi" id="MathJax-Span-5821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5822" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5823"><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-5824" 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-5825" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-315">act_1</script>, that is, <span class="MathJax_Preview">(evt,act_1)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-316-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5826"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5827"><span class="mo" id="MathJax-Span-5828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5829" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5830" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5832" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5833" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5834" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5835"><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-5836" 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-5837" 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-5838" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5839" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5840" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5843" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5844" 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-5845" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5846" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5847" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5848" 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-5849" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5850" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5851" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5852" 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-5853" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5854" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5855" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-316">(evt,act_1)
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-304-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5674"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5675"><span class="msubsup" id="MathJax-Span-5676"><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-5677" 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-5678" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-304">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-305-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5679"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5680"><span class="mi" id="MathJax-Span-5681" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5682" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5683"><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-5684" 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-5685" 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-5686" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5687" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5688" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5689"><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-5690" 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-5691" 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-5692" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5693" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5694" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5695" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5696" 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-5697" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5698" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5699" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5700" 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-5701" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5702" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5703" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-305">act_1 = \rho(a_1) \in Activities</script>.
+</li>
+<li>The event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-306-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5704"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5705"><span class="mi" id="MathJax-Span-5706" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5707" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5708" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-306">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-307-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5709"><span style="display: inline-block; position: relative; width: 35px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5710"><span class="mi" id="MathJax-Span-5711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5712" 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-5713" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5714" 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-5715" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-307">start</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-308-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5716"><span style="display: inline-block; position: relative; width: 125px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5717"><span class="mi" id="MathJax-Span-5718" 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-5719" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-5720" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-5721" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5722" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5723" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5724" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5725" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5726" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5727" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5728" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-5729" 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-5730" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5731" 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-5732" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-308">type(evt) = start</script>.
+</li>
+<li>The event happened at the start of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-309-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5733"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5734"><span class="mi" id="MathJax-Span-5735" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5736" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5737"><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-5738" 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-5739" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-309">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-310-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5740"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5741"><span class="mo" id="MathJax-Span-5742" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5743" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5744" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5745" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5746" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5747" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5748" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5749"><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-5750" 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-5751" 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-5752" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5753" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5754" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5755" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5757" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5758" 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-5759" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5760" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5761" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5762" 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-5763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5764" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5765" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5766" 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-5767" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5769" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-310">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-311-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5770"><span style="display: inline-block; position: relative; width: 234px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5771"><span class="mi" id="MathJax-Span-5772" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5773" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5774" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-5775" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5776" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-5777" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5778" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-5779" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5780" 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-5781" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5782" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5783" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5784" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5785" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5786" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5787"><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-5788" 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-5789" 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-5790" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5791" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5792" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5793" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-5794" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5795" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5796" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-5797" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5798" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5799" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5800" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5801" 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-311">min(lifetime(act_2)) = time(evt)</script>.
+</li>
+<li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-312-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5802"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5803"><span class="mi" id="MathJax-Span-5804" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-312">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-313-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5805"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5806"><span class="mi" id="MathJax-Span-5807" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5808" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5809"><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-5810" 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-5811" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-313">act_1</script> and started <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-314-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5812"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5813"><span class="mi" id="MathJax-Span-5814" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5815" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5816"><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-5817" 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-5818" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></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" id="MathJax-Element-315-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5819"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5820"><span class="mi" id="MathJax-Span-5821" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5822" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5823"><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-5824" 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-5825" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-315">act_1</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-316-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5826"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5827"><span class="mo" id="MathJax-Span-5828" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5829" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5830" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5831" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5832" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5833" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5834" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5835"><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-5836" 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-5837" 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-5838" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5839" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5840" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5842" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5843" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5844" 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-5845" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5846" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-5847" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5848" 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-5849" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5850" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5851" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5852" 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-5853" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5854" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5855" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-316">(evt,act_1)
   \in EventsActivities</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-317-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5856"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5857"><span class="mi" id="MathJax-Span-5858" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5860" 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-5861" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5862" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5863" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5864" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5865" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5866" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5867" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5869" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5870" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5871" 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-5872" 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-5873" 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-5874" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5875" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-317-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5856"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5857"><span class="mi" id="MathJax-Span-5858" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-5859" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5860" 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-5861" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5862" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-5863" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5864" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5865" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5866" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-5867" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5868" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5869" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5870" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5871" 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-5872" 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-5873" 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-5874" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5875" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-317">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">wasEndedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-318-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5876"><span style="display: inline-block; position: relative; width: 241px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5877"><span class="mi" id="MathJax-Span-5878" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5879" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5880" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5881" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5883" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5884" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5885" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5886" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5887" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5888" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5889" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5890" 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-5891" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5892" 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-5893" 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-5894" 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-5895" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5896" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5897" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5898" 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-5899" 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-5900" 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-5901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5903" 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-5904" 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-5905" 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-5906" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5907" 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-318">wasEndedBy(id,a_2,e,a_1,attrs)</script> is interpreted as follows:</p>
+<p>An activity end formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-318-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5876"><span style="display: inline-block; position: relative; width: 241px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5877"><span class="mi" id="MathJax-Span-5878" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-5879" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5880" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5881" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5883" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5884" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5885" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5886" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5887" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5888" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5889" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5890" 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-5891" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5892" 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-5893" 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-5894" 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-5895" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5896" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5897" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5898" 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-5899" 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-5900" 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-5901" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5902" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5903" 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-5904" 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-5905" 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-5906" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5907" 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-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>
-  <span class="MathJax_Preview">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-319-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5908"><span style="display: inline-block; position: relative; width: 301px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5909"><span class="mi" id="MathJax-Span-5910" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5913" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5914" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5915" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5916" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5917" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5918" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5919" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5920" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5921" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5922" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5923" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5924" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5925" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5926" 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-5927" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5928" 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-5929" 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-5930" 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-5931" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5932" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5933" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5934" 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-5935" 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-5936" 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-5937" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5938" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5939" 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-5940" 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-5941" 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-5942" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5943" 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-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" id="MathJax-Element-319-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5908"><span style="display: inline-block; position: relative; width: 301px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5909"><span class="mi" id="MathJax-Span-5910" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-5911" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5912" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-5913" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-5914" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-5915" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5916" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-5917" style="font-family: STIXGeneral-Italic;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5918" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5919" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5920" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5921" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-5922" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-5923" style="font-family: STIXGeneral-Italic;">y</span><span class="mo" id="MathJax-Span-5924" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5925" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5926" 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-5927" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5928" 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-5929" 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-5930" 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-5931" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5932" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-5933" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-5934" 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-5935" 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-5936" 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-5937" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-5938" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-5939" 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-5940" 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-5941" 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-5942" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-5943" 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-319">W,\rho \models wasEndedBy(id,a_2,e,a_1,attrs)</script> holds if and only
   if:</p>
   
 <ol>
-  <li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processed" id="MathJax-Element-320-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5944"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5945"><span class="mi" id="MathJax-Span-5946" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5947" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-320">id</script> denotes an event <span class="MathJax_Preview">evt = \rho(id) \in Events</span><span class="MathJax MathJax_Processed" id="MathJax-Element-321-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5948"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5949"><span class="mi" id="MathJax-Span-5950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5951" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5953" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5954" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5955" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5956" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5957" 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-5958" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5959" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5960" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5961" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5962" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5963" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5964" 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-5965" style="font-family: STIXGeneral-Italic;">s</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-321">evt = \rho(id) \in Events</script>.</li>
-<li> [WF] <span class="MathJax_Preview">a_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-322-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5966"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5967"><span class="msubsup" id="MathJax-Span-5968"><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-5969" 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-5970" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-322">a_2</script> denotes an activity <span class="MathJax_Preview">act_2 = \rho(a_2)\in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-323-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5971"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5972"><span class="mi" id="MathJax-Span-5973" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5974" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5975"><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-5976" 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-5977" 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-5978" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5979" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5980" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5981"><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-5982" 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-5983" 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-5984" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5985" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5986" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5987" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5988" 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-5989" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5990" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5991" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5992" 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-5993" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5995" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-323">act_2 = \rho(a_2)\in Activities</script>.</li>
-<li> [WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-324-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5996"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5997"><span class="mi" id="MathJax-Span-5998" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-324">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e)\in Entities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-325-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5999"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6000"><span class="mi" id="MathJax-Span-6001" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6002" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6003" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6004" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6005" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6006" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6007" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6008" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6009" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6010" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6011" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6012" 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-6013" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6014" 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-6015" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6016" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6017" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-325">ent = \rho(e)\in Entities</script>.</li>
-<li>[WF] <span class="MathJax_Preview">a_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-326-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6018"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-6019"><span class="msubsup" id="MathJax-Span-6020"><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-6021" 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-6022" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-326">a_1</script> denotes an activity <span class="MathJax_Preview">act_1 = \rho(a_1)\in Activities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-327-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6023"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6024"><span class="mi" id="MathJax-Span-6025" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6026" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6027"><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-6028" 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-6029" 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-6030" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6031" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6032" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6033"><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-6034" 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-6035" 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-6036" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6037" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6038" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6039" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6040" 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-6041" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6042" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6044" 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-6045" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6046" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6047" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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">evt</span><span class="MathJax MathJax_Processed" id="MathJax-Element-328-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6048"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6049"><span class="mi" id="MathJax-Span-6050" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6051" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-328">evt</script> has type <span class="MathJax_Preview">end</span><span class="MathJax MathJax_Processed" id="MathJax-Element-329-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6053"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6054"><span class="mi" id="MathJax-Span-6055" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6056" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6057" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-329">end</script>, i.e. <span class="MathJax_Preview">type(evt) = end</span><span class="MathJax MathJax_Processed" id="MathJax-Element-330-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6058"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6059"><span class="mi" id="MathJax-Span-6060" 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-6061" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6062" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6063" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6064" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6065" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6066" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6068" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6069" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6070" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6071" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6072" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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-330">type(evt) = end</script>.</li>
-<li>The event happened at the end of <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-331-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6073"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6074"><span class="mi" id="MathJax-Span-6075" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6076" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6077"><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-6078" 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-6079" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-331">act_2</script>, that is, <span class="MathJax_Preview">(evt,act_2)
-  \in EventsActivities</span><span class="MathJax MathJax_Processed" id="MathJax-Element-332-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6080"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6081"><span class="mo" id="MathJax-Span-6082" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6083" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6084" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6085" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6086" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6087" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6088" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6089"><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-6090" 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-6091" 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-6092" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6093" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6094" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6095" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6096" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6097" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6098" 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-6099" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6100" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6101" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6102" 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-6103" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6104" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6105" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6106" 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-6107" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6108" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6109" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-332">(evt,act_2)
-  \in EventsActivities</script>, and <span class="MathJax_Preview">max(lifetime(act_2)) = time(evt)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-333-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6110"><span style="display: inline-block; position: relative; width: 237px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6111"><span class="mi" id="MathJax-Span-6112" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6113" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6114" 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-6115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6116" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6117" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6118" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6119" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6120" 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-6121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6122" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6123" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6124" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6125" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6126" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6127"><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-6128" 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-6129" 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-6130" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6131" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6132" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6133" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6134" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6135" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6136" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6137" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6138" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6139" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6140" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6141" 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-333">max(lifetime(act_2)) = time(evt)</script>.</li>
-  <li>TODO: The entity <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processed" id="MathJax-Element-334-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6142"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6143"><span class="mi" id="MathJax-Span-6144" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-334">e</script> was generated by <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-335-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6145"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6146"><span class="mi" id="MathJax-Span-6147" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6148" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6149"><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-6150" 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-6151" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-335">act_1</script> and ended <span class="MathJax_Preview">act_2</span><span class="MathJax MathJax_Processed" id="MathJax-Element-336-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6152"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6153"><span class="mi" id="MathJax-Span-6154" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6155" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6156"><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-6157" 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-6158" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-336">act_2</script>.</li>
-
-<li>The event happened during <span class="MathJax_Preview">act_1</span><span class="MathJax MathJax_Processed" id="MathJax-Element-337-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6159"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6160"><span class="mi" id="MathJax-Span-6161" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6162" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6163"><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-6164" 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-6165" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></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">match(W,evt,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-338-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6166"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6167"><span class="mi" id="MathJax-Span-6168" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6169" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6170" 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-6171" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6172" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6173" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6174" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6175" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6176" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6177" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6178" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6179" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6180" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6181" 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-6182" 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-6183" 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-6184" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6185" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-320-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5944"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5945"><span class="mi" id="MathJax-Span-5946" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5947" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-320">id</script> denotes an event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-321-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5948"><span style="display: inline-block; position: relative; width: 158px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5949"><span class="mi" id="MathJax-Span-5950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5951" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5952" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-5953" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5954" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5955" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-5956" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5957" 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-5958" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5959" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5960" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-5961" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5962" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5963" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-5964" 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-5965" style="font-family: STIXGeneral-Italic;">s</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-321">evt = \rho(id) \in Events</script>.</li>
+<li> [WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-322-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5966"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-5967"><span class="msubsup" id="MathJax-Span-5968"><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-5969" 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-5970" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-322">a_2</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-323-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5971"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5972"><span class="mi" id="MathJax-Span-5973" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-5974" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-5975"><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-5976" 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-5977" 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-5978" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-5979" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-5980" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-5981"><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-5982" 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-5983" 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-5984" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-5985" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-5986" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-5987" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-5988" 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-5989" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5990" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-5991" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5992" 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-5993" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-5994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-5995" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-324-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5996"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-5997"><span class="mi" id="MathJax-Span-5998" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-324">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-325-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-5999"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6000"><span class="mi" id="MathJax-Span-6001" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6002" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6003" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6004" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6005" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6006" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6007" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6008" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6009" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6010" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6011" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6012" 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-6013" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6014" 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-6015" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6016" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6017" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-326-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6018"><span style="display: inline-block; position: relative; width: 19px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.7px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-6019"><span class="msubsup" id="MathJax-Span-6020"><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-6021" 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-6022" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-326">a_1</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-327-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6023"><span style="display: inline-block; position: relative; width: 190px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6024"><span class="mi" id="MathJax-Span-6025" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6026" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6027"><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-6028" 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-6029" 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-6030" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6031" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6032" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6033"><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-6034" 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-6035" 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-6036" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6037" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6038" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6039" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6040" 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-6041" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6042" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6043" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6044" 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-6045" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6046" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6047" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-328-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6048"><span style="display: inline-block; position: relative; width: 22px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6049"><span class="mi" id="MathJax-Span-6050" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6051" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6052" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-328">evt</script> has type <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-329-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6053"><span style="display: inline-block; position: relative; width: 29px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6054"><span class="mi" id="MathJax-Span-6055" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6056" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6057" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-329">end</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-330-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6058"><span style="display: inline-block; position: relative; width: 119px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6059"><span class="mi" id="MathJax-Span-6060" 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-6061" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6062" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6063" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6064" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6065" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6066" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6067" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6068" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6069" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6070" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6071" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6072" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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-330">type(evt) = end</script>.</li>
+<li>The event happened at the end of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-331-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6073"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6074"><span class="mi" id="MathJax-Span-6075" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6076" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6077"><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-6078" 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-6079" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-331">act_2</script>, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-332-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6080"><span style="display: inline-block; position: relative; width: 216px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 54.4px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6081"><span class="mo" id="MathJax-Span-6082" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6083" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6084" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6085" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6086" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6087" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6088" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6089"><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-6090" 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-6091" 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-6092" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6093" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6094" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6095" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6096" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6097" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6098" 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-6099" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6100" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6101" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6102" 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-6103" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6104" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6105" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6106" 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-6107" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6108" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6109" style="font-family: STIXGeneral-Italic;">s</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: 18.5px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-332">(evt,act_2)
+  \in EventsActivities</script>, and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-333-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6110"><span style="display: inline-block; position: relative; width: 237px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6111"><span class="mi" id="MathJax-Span-6112" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6113" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6114" 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-6115" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6116" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6117" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6118" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6119" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6120" 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-6121" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6122" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6123" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6124" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6125" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6126" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6127"><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-6128" 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-6129" 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-6130" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6131" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6132" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6133" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-6134" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6135" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6136" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6137" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6138" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6139" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6140" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6141" 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-333">max(lifetime(act_2)) = time(evt)</script>.</li>
+  <li>TODO: The entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-334-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6142"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6143"><span class="mi" id="MathJax-Span-6144" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-334">e</script> was generated by <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-335-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6145"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6146"><span class="mi" id="MathJax-Span-6147" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6148" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6149"><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-6150" 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-6151" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-335">act_1</script> and ended <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-336-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6152"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6153"><span class="mi" id="MathJax-Span-6154" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6155" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6156"><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-6157" 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-6158" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></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" id="MathJax-Element-337-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6159"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6160"><span class="mi" id="MathJax-Span-6161" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6162" style="font-family: STIXGeneral-Italic;">c</span><span class="msubsup" id="MathJax-Span-6163"><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-6164" 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-6165" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></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" id="MathJax-Element-338-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6166"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6167"><span class="mi" id="MathJax-Span-6168" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6169" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6170" 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-6171" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6172" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6173" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6174" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6175" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6176" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6177" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6178" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6179" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6180" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6181" 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-6182" 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-6183" 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-6184" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6185" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-338">match(W,evt,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1846,23 +1842,23 @@
 <h4><span class="secno">4.4.7 </span> Attribution </h4>
 
 <p>
-An attribution formula <span class="MathJax_Preview">wasAttributedTo(id,e,ag,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-339-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6186"><span style="display: inline-block; position: relative; width: 246px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6187"><span class="mi" id="MathJax-Span-6188" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6189" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6190" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6191" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6192" 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-6193" 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-6194" 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-6195" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6196" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6197" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6198" 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-6199" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6200" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6201" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6202" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6203" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6204" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6205" 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-6206" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6207" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6208" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6209" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6210" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6211" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6212" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6213" 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-6214" 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-6215" 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-6216" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6217" 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-339">wasAttributedTo(id,e,ag,attrs)</script> is interpreted as follows:
+An attribution formula <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-339-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6186"><span style="display: inline-block; position: relative; width: 246px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6187"><span class="mi" id="MathJax-Span-6188" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6189" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6190" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6191" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6192" 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-6193" 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-6194" 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-6195" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6196" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6197" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6198" 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-6199" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6200" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6201" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6202" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6203" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6204" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6205" 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-6206" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6207" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6208" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6209" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6210" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6211" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6212" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6213" 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-6214" 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-6215" 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-6216" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6217" 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-339">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>
   <p>
-  <span class="MathJax_Preview">W,\rho \models wasAttributedTo(id,e,ag,attrs)</span><span class="MathJax MathJax_Processed" id="MathJax-Element-340-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6218"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6219"><span class="mi" id="MathJax-Span-6220" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6221" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6222" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6223" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6224" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6226" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6227" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6228" 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-6229" 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-6230" 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-6231" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6232" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6233" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6234" 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-6235" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6236" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6237" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6238" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6239" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6240" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6241" 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-6242" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6243" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6244" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6245" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6246" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6247" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6248" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6249" 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-6250" 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-6251" 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-6252" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6253" 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-340">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-340-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6218"><span style="display: inline-block; position: relative; width: 306px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6219"><span class="mi" id="MathJax-Span-6220" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6221" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6222" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6223" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6224" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6225" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6226" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6227" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6228" 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-6229" 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-6230" 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-6231" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6232" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6233" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6234" 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-6235" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6236" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6237" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6238" style="font-family: STIXGeneral-Italic;">o</span><span class="mo" id="MathJax-Span-6239" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6240" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6241" 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-6242" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6243" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-6244" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6245" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6246" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6247" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6248" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6249" 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-6250" 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-6251" 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-6252" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6253" 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-340">W,\rho \models wasAttributedTo(id,e,ag,attrs)</script>
   holds if and only if:
   </p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-341-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-341">id</script> denotes an association <span class="MathJax_Preview">assoc = \rho(id) \in Associations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-342-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-342">assoc = \rho(id) \in Associations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e</span><span class="MathJax MathJax_Processing" id="MathJax-Element-343-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-343">e</script> denotes an entity <span class="MathJax_Preview">ent = \rho(e) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-344-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-341-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6254"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6255"><span class="mi" id="MathJax-Span-6256" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6257" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-341">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-342-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6258"><span style="display: inline-block; position: relative; width: 224px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6259"><span class="mi" id="MathJax-Span-6260" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6261" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6262" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6263" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6264" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6265" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6266" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6267" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6268" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6269" 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-6270" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6271" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6272" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6273" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6274" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6275" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6276" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6277" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6278" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6279" 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-6280" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6281" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6282" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6283" style="font-family: STIXGeneral-Italic;">s</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-342">assoc = \rho(id) \in Associations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag</span><span class="MathJax MathJax_Processing" id="MathJax-Element-345-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-345">ag</script> denotes an agent <span class="MathJax_Preview">agent = \rho(ag) \in Agents</span><span class="MathJax MathJax_Processing" id="MathJax-Element-346-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-343-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6284"><span style="display: inline-block; position: relative; width: 8px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6285"><span class="mi" id="MathJax-Span-6286" style="font-family: STIXGeneral-Italic;">e</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-343">e</script> denotes an entity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-344-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6287"><span style="display: inline-block; position: relative; width: 160px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6288"><span class="mi" id="MathJax-Span-6289" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6290" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6291" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6292" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6293" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6294" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6295" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6296" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6297" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6298" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6299" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6300" 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-6301" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6302" 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-6303" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6304" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6305" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-344">ent = \rho(e) \in Entities</script>.
 </li>
-<li>The entity was attributed to the agent, i.e. <span class="MathJax_Preview">(assoc,ent,agent) \in AttributedTo</span><span class="MathJax MathJax_Processing" id="MathJax-Element-347-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-345-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6306"><span style="display: inline-block; position: relative; width: 20px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6307"><span class="mi" id="MathJax-Span-6308" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6309" style="font-family: STIXGeneral-Italic;">g</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: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-345">ag</script> denotes an agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-346-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6310"><span style="display: inline-block; position: relative; width: 186px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6311"><span class="mi" id="MathJax-Span-6312" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6313" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6314" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6315" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6316" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6317" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6318" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6319" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6320" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6321" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6322" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6323" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6324" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6325" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6326" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6327" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6328" 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-6329" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-346">agent = \rho(ag) \in Agents</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,evt,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-348-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-347-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6330"><span style="display: inline-block; position: relative; width: 261px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6331"><span class="mo" id="MathJax-Span-6332" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6333" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6334" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6335" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6336" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6337" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6338" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6339" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6340" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6341" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6342" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6343" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6344" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6345" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6346" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6347" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6348" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6349" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6350" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6351" 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-6352" 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-6353" 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-6354" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6355" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-6356" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-6357" 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-6358" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6359" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6360" style="font-family: STIXGeneral-Italic;">T<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.5px;"></span></span><span class="mi" id="MathJax-Span-6361" style="font-family: STIXGeneral-Italic;">o</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-347">(assoc,ent,agent) \in AttributedTo</script>.
+</li>
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-348-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6362"><span style="display: inline-block; position: relative; width: 149px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6363"><span class="mi" id="MathJax-Span-6364" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6365" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6366" 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-6367" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6368" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6369" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6370" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6371" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6372" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6373" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6374" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6375" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6376" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6377" 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-6378" 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-6379" 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-6380" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6381" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-348">match(W,evt,attrs)</script>.
 </li></ol>
 </div>
 </section>
@@ -1878,21 +1874,21 @@
 
 <h4><span class="secno">4.4.9 </span> Responsibility </h4>
 
-<p>The <span class="MathJax_Preview">actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-349-Frame" role="textbox" aria-readonly="true"></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">ActsFor</span><span class="MathJax MathJax_Processing" id="MathJax-Element-350-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-350">ActsFor</script> relation as follows:</p>
+<p>The <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-349-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6382"><span style="display: inline-block; position: relative; width: 316px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6383"><span class="mi" id="MathJax-Span-6384" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6385" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6386" 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-6387" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6388" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6389" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6390" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6391" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-6392" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6393" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-6394" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6395" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6396" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6397" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6398" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-6399" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6400" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6401" 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-6402" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6403" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6404"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6405" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6406" 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-6407" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6408" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6409"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6410" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6411" 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-6412" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6413" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6414" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6415" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6416" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6417" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6418" 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-6419" 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-6420" 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-6421" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6422" 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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-350-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6423"><span style="display: inline-block; position: relative; width: 63px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.1px 19360px 51.3px -10px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6424"><span class="mi" id="MathJax-Span-6425" style="font-family: STIXGeneral-Italic;">A</span><span class="mi" id="MathJax-Span-6426" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6427" 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-6428" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6429" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6430" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6431" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></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: 15.2px; vertical-align: -1.3px;"></span></span></nobr></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>
-  <span class="MathJax_Preview">W,\rho \models actedOnBehalfOf(id,ag_2,ag_1,act,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-351-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-351-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6432"><span style="display: inline-block; position: relative; width: 375px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6433"><span class="mi" id="MathJax-Span-6434" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6435" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6436" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6437" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6438" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-6439" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6440" 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-6441" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6442" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6443" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6444" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6445" style="font-family: STIXGeneral-Italic;">B</span><span class="mi" id="MathJax-Span-6446" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6447" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-6448" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6449" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6450" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-6451" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-6452" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-6453" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6454" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6455" 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-6456" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6457" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6458"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6459" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6460" 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-6461" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6462" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6463"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6464" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6465" 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-6466" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6467" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6468" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6469" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6470" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6471" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6472" 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-6473" 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-6474" 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-6475" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6476" 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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-352-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-352">id</script> denotes an association <span class="MathJax_Preview">deleg=\rho(id) \in Delegations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-353-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-353">deleg=\rho(id) \in Delegations</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-352-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6477"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6478"><span class="mi" id="MathJax-Span-6479" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6480" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-352">id</script> denotes an association <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-353-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6481"><span style="display: inline-block; position: relative; width: 220px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6482"><span class="mi" id="MathJax-Span-6483" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6484" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6485" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6486" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6487" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6488" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6489" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6490" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6491" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6492" 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-6493" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6494" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6495" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-6496" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6497" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6498" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6499" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6500" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6501" 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-6502" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6503" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6504" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6505" style="font-family: STIXGeneral-Italic;">s</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-353">deleg=\rho(id) \in Delegations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-354-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-354">a</script> denotes an activity <span class="MathJax_Preview">act=\rho(a) \in Activities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-355-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-354-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6506"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6507"><span class="mi" id="MathJax-Span-6508" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-354">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-355-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6509"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6510"><span class="mi" id="MathJax-Span-6511" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6512" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6513" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6514" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6515" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6516" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6517" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-6518" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6519" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6520" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6521" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6522" 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-6523" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6524" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6525" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6526" 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-6527" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6528" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6529" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-355">act=\rho(a) \in Activities</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">ag_1,ag_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-356-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-356">ag_1,ag_2</script> denote agents <span class="MathJax_Preview">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</span><span class="MathJax MathJax_Processing" id="MathJax-Element-357-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-356-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6530"><span style="display: inline-block; position: relative; width: 65px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6531"><span class="mi" id="MathJax-Span-6532" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6533"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6534" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6535" 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-6536" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6537" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="msubsup" id="MathJax-Span-6538"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6539" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6540" 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><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: 15.2px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-356">ag_1,ag_2</script> denote agents <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-357-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6541"><span style="display: inline-block; position: relative; width: 339px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55.7px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6542"><span class="mi" id="MathJax-Span-6543" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6544" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6545" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6546" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6547"><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-6548" 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-6549" 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-6550" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6551" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6552" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6553" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6554"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6555" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6556" 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-6557" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6558" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6559" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6560" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6561" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6562" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6563"><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-6564" 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-6565" 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-6566" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6567" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6568" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6569" style="font-family: STIXGeneral-Italic;">a</span><span class="msubsup" id="MathJax-Span-6570"><span style="display: inline-block; position: relative; width: 18.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6571" style="font-family: STIXGeneral-Italic;">g</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 10px;"><span class="mn" id="MathJax-Span-6572" 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-6573" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6574" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6575" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6576" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6577" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6578" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6579" 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-6580" style="font-family: STIXGeneral-Italic;">s</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: 19.8px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-357">agent_1=\rho(ag_1), agent_2=\rho(ag_2) \in Agents</script>.
 </li>
-<li>The agent <span class="MathJax_Preview">agent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-358-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-358">agent_2</script> acts for the agent <span class="MathJax_Preview">agent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-359-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-359">agent_1</script> with respect to the activity <span class="MathJax_Preview">act</span><span class="MathJax MathJax_Processing" id="MathJax-Element-360-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-360">act</script>, i.e. <span class="MathJax_Preview">(deleg,agent_2,agent_1,act) \in ActsFor</span><span class="MathJax MathJax_Processing" id="MathJax-Element-361-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-361">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
+<li>The agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-358-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6581"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6582"><span class="mi" id="MathJax-Span-6583" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6584" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6585" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6586" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6587"><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-6588" 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-6589" 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><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: 16.6px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-358">agent_2</script> acts for the agent <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-359-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6590"><span style="display: inline-block; position: relative; width: 53px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6591"><span class="mi" id="MathJax-Span-6592" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6593" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6594" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6595" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6596"><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-6597" 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-6598" 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><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: 16.6px; vertical-align: -5px;"></span></span></nobr></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" id="MathJax-Element-360-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6599"><span style="display: inline-block; position: relative; width: 24px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6600"><span class="mi" id="MathJax-Span-6601" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6602" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6603" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-360">act</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-361-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6604"><span style="display: inline-block; position: relative; width: 291px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6605"><span class="mo" id="MathJax-Span-6606" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6607" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6608" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6609" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-6610" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6611" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6612" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6613" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6614" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6615" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6616" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6617"><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-6618" 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-6619" 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-6620" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6621" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6622" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6623" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6624" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6625"><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-6626" 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-6627" 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-6628" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6629" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6630" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6631" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6632" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6633" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6634" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6635" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6636" 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-6637" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6638" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6639" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6640" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></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-361">(deleg,agent_2,agent_1,act) \in ActsFor</script>.
 </li>
-<li>The attributes match: <span class="MathJax_Preview">match(W,assoc,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-362-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-362">match(W,assoc,attrs)</script>.
+<li>The attributes match: <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-362-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6641"><span style="display: inline-block; position: relative; width: 170px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6642"><span class="mi" id="MathJax-Span-6643" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6644" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6645" 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-6646" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6647" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6648" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6649" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6650" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6651" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6652" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6653" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6654" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6655" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-6656" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6657" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6658" 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-6659" 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-6660" 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-6661" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6662" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-362">match(W,assoc,attrs)</script>.
 </li></ol></div>
 </section>
 
@@ -1904,26 +1900,25 @@
 <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">wasDerivedFrom(id,e_2,e_1,a,g,u,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-363-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-363-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6663"><span style="display: inline-block; position: relative; width: 309px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6664"><span class="mi" id="MathJax-Span-6665" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6666" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6667" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6668" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6669" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6670" 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-6671" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6672" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6673" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6674" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6675" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6676" 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-6677" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6678" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6679" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6680" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6681" 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-6682" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6683" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6684" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6685" 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-6686" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6687" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6688" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6689" 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-6690" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6691" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mo" id="MathJax-Span-6692" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6693" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-6694" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6695" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-6696" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6697" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6698" 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-6699" 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-6700" 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-6701" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6702" 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-363">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">W,\rho \models wasDerivedFrom(id,e_2,e_1,act,g,u,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-364-Frame" role="textbox" aria-readonly="true"></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>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-364-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6703"><span style="display: inline-block; position: relative; width: 382px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6704"><span class="mi" id="MathJax-Span-6705" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6706" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6707" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-6708" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-6709" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-6710" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6711" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6712" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6713" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6714" 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-6715" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6716" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6717" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6718" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6719" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6720" 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-6721" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6722" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6723" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6724" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6725" 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-6726" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6727" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6728" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6729" 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-6730" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6731" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6732" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6733" 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-6734" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6735" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6736" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6737" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6738" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6739" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">g</span><span class="mo" id="MathJax-Span-6740" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6741" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">u</span><span class="mo" id="MathJax-Span-6742" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6743" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6744" 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-6745" 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-6746" 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-6747" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6748" 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-364">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">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-365-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-365">id</script> denotes a derivation <span class="MathJax_Preview">deriv = \rho(id) \in Derivations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-366-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-366">deriv = \rho(id) \in Derivations</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">e_1,e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-367-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-367">e_1,e_2</script> denote entities <span class="MathJax_Preview">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-368-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-368">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> .
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-365-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6749"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6750"><span class="mi" id="MathJax-Span-6751" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6752" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-365">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-366-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6753"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6754"><span class="mi" id="MathJax-Span-6755" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6756" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6757" 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-6758" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6759" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6760" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6761" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6762" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6763" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6764" 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-6765" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6766" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6767" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-6768" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6769" 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-6770" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6771" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6772" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6773" 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-6774" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6775" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6776" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6777" style="font-family: STIXGeneral-Italic;">s</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-366">deriv = \rho(id) \in Derivations</script>.
 </li>
-<li>[WF] <span class="MathJax_Preview">a</span><span class="MathJax MathJax_Processing" id="MathJax-Element-369-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-369">a</script> denotes an activity <span class="MathJax_Preview">act = \rho(a) \in Activities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-370-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-370">act = \rho(a) \in Activities</script>.
-</li>
-<li>[WF] <span class="MathJax_Preview">g</span><span class="MathJax MathJax_Processing" id="MathJax-Element-371-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-371">g</script> denotes a generation event <span class="MathJax_Preview">gen = \rho(g) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-372-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-372">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview">type(\rho(g)) = generation</span><span class="MathJax MathJax_Processing" id="MathJax-Element-373-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-373">type(\rho(g)) = generation</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-367-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6778"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6779"><span class="msubsup" id="MathJax-Span-6780"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6781" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6782" 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-6783" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-6784" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6785" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6786" 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><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: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-367">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-368-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6787"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6788"><span class="mi" id="MathJax-Span-6789" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6790" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6791"><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-6792" 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-6793" 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-6794" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6795" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6796" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6797"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6798" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6799" 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-6800" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6801" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6802" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-6803" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6804"><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-6805" 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-6806" 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-6807" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6808" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6809" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-6810"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-6811" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-6812" 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-6813" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6814" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6815" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6816" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6817" 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-6818" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6819" 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-6820" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6821" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6822" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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">u</span><span class="MathJax MathJax_Processing" id="MathJax-Element-374-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-374">u</script> denotes a use event <span class="MathJax_Preview">\rho(u) \in Events</span><span class="MathJax MathJax_Processing" id="MathJax-Element-375-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-375">\rho(u) \in Events</script> and <span class="MathJax_Preview">type(\rho(u)) = use</span><span class="MathJax MathJax_Processing" id="MathJax-Element-376-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-376">type(\rho(u)) = use</script>.
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-369-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6823"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6824"><span class="mi" id="MathJax-Span-6825" style="font-family: STIXGeneral-Italic;">a</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-369">a</script> denotes an activity <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-370-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6826"><span style="display: inline-block; position: relative; width: 172px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6827"><span class="mi" id="MathJax-Span-6828" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6829" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6830" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6831" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6832" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6833" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6834" style="font-family: STIXGeneral-Italic;">a</span><span class="mo" id="MathJax-Span-6835" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6836" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6837" style="font-family: STIXGeneral-Italic; padding-left: 6px;">A</span><span class="mi" id="MathJax-Span-6838" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6839" 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-6840" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6841" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6842" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6843" 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-6844" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6845" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6846" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-370">act = \rho(a) \in Activities</script>.
 </li>
-<li>The derivation denotes a one-step derivation <span class="MathJax_Preview">derivedFrom(deriv) =
-ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-377-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-377">derivedFrom(deriv) =
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-371-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6847"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6848"><span class="mi" id="MathJax-Span-6849" style="font-family: STIXGeneral-Italic;">g</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: 14.5px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-371">g</script> denotes a generation event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-372-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6850"><span style="display: inline-block; position: relative; width: 159px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6851"><span class="mi" id="MathJax-Span-6852" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-6853" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6854" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-6855" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6856" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-6857" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6858" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6859" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6860" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6861" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6862" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6863" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6864" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6865" 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-6866" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-372">gen = \rho(g) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-373-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6867"><span style="display: inline-block; position: relative; width: 184px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6868"><span class="mi" id="MathJax-Span-6869" 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-6870" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6871" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6872" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6873" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6874" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6875" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6876" style="font-family: STIXGeneral-Italic;">g</span><span class="mo" id="MathJax-Span-6877" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6878" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6879" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6880" style="font-family: STIXGeneral-Italic; padding-left: 6px;">g</span><span class="mi" id="MathJax-Span-6881" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6882" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6883" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6884" 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-6885" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6886" 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-6887" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6888" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6889" style="font-family: STIXGeneral-Italic;">n</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-373">type(\rho(g)) = generation</script>.
+</li>
+<li>[WF] <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-374-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6890"><span style="display: inline-block; position: relative; width: 10px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6891"><span class="mi" id="MathJax-Span-6892" style="font-family: STIXGeneral-Italic;">u</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: 10.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-374">u</script> denotes a use event <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-375-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6893"><span style="display: inline-block; position: relative; width: 106px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -9.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6894"><span class="mi" id="MathJax-Span-6895" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6896" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6897" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-6898" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6899" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-6900" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-6901" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6902" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6903" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-6904" 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-6905" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-375">\rho(u) \in Events</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-376-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6906"><span style="display: inline-block; position: relative; width: 126px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6907"><span class="mi" id="MathJax-Span-6908" 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-6909" style="font-family: STIXGeneral-Italic;">y</span><span class="mi" id="MathJax-Span-6910" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-6911" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6912" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6913" style="font-family: STIXGeneral-Italic;">ρ</span><span class="mo" id="MathJax-Span-6914" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6915" style="font-family: STIXGeneral-Italic;">u</span><span class="mo" id="MathJax-Span-6916" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6917" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6918" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6919" style="font-family: STIXGeneral-Italic; padding-left: 6px;">u</span><span class="mi" id="MathJax-Span-6920" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6921" style="font-family: STIXGeneral-Italic;">e</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-376">type(\rho(u)) = use</script>.
+</li>
+<li>The derivation denotes a one-step derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-377-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6922"><span style="display: inline-block; position: relative; width: 382px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6923"><span class="mi" id="MathJax-Span-6924" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6925" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6926" 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-6927" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6928" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6929" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6930" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6931" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-6932" 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-6933" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-6934" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-6935" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6936" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6937" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6938" 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-6939" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6940" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6941" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-6942" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-6943" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-6944" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6945"><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-6946" 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-6947" 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-6948" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6949" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">g</span><span class="mi" id="MathJax-Span-6950" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6951" style="font-family: STIXGeneral-Italic;">n</span><span class="mo" id="MathJax-Span-6952" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6953" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">a</span><span class="mi" id="MathJax-Span-6954" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6955" style="font-family: STIXGeneral-Italic;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mo" id="MathJax-Span-6956" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6957" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">u</span><span class="mi" id="MathJax-Span-6958" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6959" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-6960" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-6961" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">e</span><span class="mi" id="MathJax-Span-6962" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-6963"><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-6964" 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-6965" 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><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-377">derivedFrom(deriv) =
 ent_2 \cdot gen \cdot act \cdot use \cdot ent_1</script>.
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,deriv,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-378-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-378-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6966"><span style="display: inline-block; position: relative; width: 167px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6967"><span class="mi" id="MathJax-Span-6968" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-6969" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6970" 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-6971" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-6972" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-6973" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-6974" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-6975" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6976" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-6977" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6978" 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-6979" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6980" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-6981" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-6982" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-6983" 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-6984" 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-6985" 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-6986" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-6987" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-378">match(W,deriv,attrs)</script>.</li>
 </ol>
 </div>
 </section>
@@ -1931,18 +1926,18 @@
 
 <h5><span class="secno">4.4.10.2 </span> Imprecise </h5>
 <p>
-An imprecise derivation formula has the form <span class="MathJax_Preview">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-379-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-379">wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script>.</p>
+An imprecise derivation formula has the form <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-379-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-6988"><span style="display: inline-block; position: relative; width: 318px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-6989"><span class="mi" id="MathJax-Span-6990" style="font-family: STIXGeneral-Italic;">w</span><span class="mi" id="MathJax-Span-6991" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-6992" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-6993" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-6994" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6995" 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-6996" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-6997" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-6998" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-6999" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7000" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7001" 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-7002" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7003" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7004" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7005" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7006" 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-7007" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7008" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7009" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7010" 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-7011" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7012" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7013" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7014" 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-7015" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7016" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7017" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7018" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7019" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7020" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7021" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7022" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7023" 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-7024" 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-7025" 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-7026" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7027" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-380-Frame" role="textbox" aria-readonly="true"></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>
+  <p><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-380-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7028"><span style="display: inline-block; position: relative; width: 377px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7029"><span class="mi" id="MathJax-Span-7030" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7031" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7032" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7033" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7034" style="font-family: STIXGeneral-Italic; padding-left: 6px;">w</span><span class="mi" id="MathJax-Span-7035" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7036" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-7037" style="font-family: STIXGeneral-Italic;">D</span><span class="mi" id="MathJax-Span-7038" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7039" 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-7040" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7041" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7042" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7043" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7044" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7045" 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-7046" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7047" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7048" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7049" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7050" 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-7051" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7052" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7053" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7054" 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-7055" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7056" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7057" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7058" 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-7059" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7060" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7061" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7062" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7063" style="font-family: STIXGeneral-Regular;">,</span><span class="mo" id="MathJax-Span-7064" style="font-family: STIXGeneral-Regular; padding-left: 3.6px;">−</span><span class="mo" id="MathJax-Span-7065" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7066" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7067" 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-7068" 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-7069" 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-7070" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7071" 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-380">W,\rho \models wasDerivedFrom(id,e_2,e_1,-,-,-,attrs)</script> holds if and only if:</p>
 <ol>
-<li>[WF] <span class="MathJax_Preview">id</span><span class="MathJax MathJax_Processing" id="MathJax-Element-381-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-381">id</script> denotes a derivation <span class="MathJax_Preview">deriv = \rho(id) \in Derivations</span><span class="MathJax MathJax_Processing" id="MathJax-Element-382-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-381-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7072"><span style="display: inline-block; position: relative; width: 16px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.1px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7073"><span class="mi" id="MathJax-Span-7074" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7075" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-381">id</script> denotes a derivation <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-382-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7076"><span style="display: inline-block; position: relative; width: 215px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7077"><span class="mi" id="MathJax-Span-7078" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7079" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7080" 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-7081" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7082" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7083" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7084" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7085" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7086" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7087" 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-7088" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7089" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7090" style="font-family: STIXGeneral-Italic; padding-left: 6px;">D</span><span class="mi" id="MathJax-Span-7091" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7092" 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-7093" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7094" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7095" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7096" 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-7097" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7098" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7099" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7100" style="font-family: STIXGeneral-Italic;">s</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-382">deriv = \rho(id) \in Derivations</script>
 </li>
-<li>[WF] <span class="MathJax_Preview">e_1,e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-383-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-383">e_1,e_2</script> denote entities <span class="MathJax_Preview">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-384-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-383-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7101"><span style="display: inline-block; position: relative; width: 41px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7102"><span class="msubsup" id="MathJax-Span-7103"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7104" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7105" 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-7106" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7107" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7108" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7109" 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><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: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-383">e_1,e_2</script> denote entities <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-384-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7110"><span style="display: inline-block; position: relative; width: 281px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7111"><span class="mi" id="MathJax-Span-7112" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7113" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7114"><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-7115" 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-7116" 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-7117" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7118" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7119" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7120"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7121" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7122" 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-7123" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7124" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7125" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mi" id="MathJax-Span-7126" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7127"><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-7128" 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-7129" 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-7130" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7131" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7132" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7133"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7134" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7135" 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-7136" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7137" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7138" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7139" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7140" 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-7141" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7142" 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-7143" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7144" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7145" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-384">ent_1 = \rho(e_1), ent_2=\rho(e_2)  \in Entities</script> 
 </li>
-<li><span class="MathJax_Preview">derivedFrom(deriv)= ent_2 \cdot  w \cdot ent_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-385-Frame" role="textbox" aria-readonly="true"></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">w</span><span class="MathJax MathJax_Processing" id="MathJax-Element-386-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-386">w</script>
+<li><span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-385-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7146"><span style="display: inline-block; position: relative; width: 287px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7147"><span class="mi" id="MathJax-Span-7148" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7149" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7150" 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-7151" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7152" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7153" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7154" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7155" style="font-family: STIXGeneral-Italic;">F<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.7px;"></span></span><span class="mi" id="MathJax-Span-7156" 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-7157" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7158" style="font-family: STIXGeneral-Italic;">m</span><span class="mo" id="MathJax-Span-7159" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7160" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7161" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7162" 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-7163" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7164" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7165" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7166" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7167" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-7168" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7169"><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-7170" 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-7171" 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-7172" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-7173" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">w</span><span class="mo" id="MathJax-Span-7174" style="font-family: STIXGeneral-Regular; padding-left: 4.8px;">⋅</span><span class="mi" id="MathJax-Span-7175" style="font-family: STIXGeneral-Italic; padding-left: 4.8px;">e</span><span class="mi" id="MathJax-Span-7176" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7177"><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-7178" 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-7179" 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><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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></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" id="MathJax-Element-386-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7180"><span style="display: inline-block; position: relative; width: 13px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(36.5px 19360px 51.3px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7181"><span class="mi" id="MathJax-Span-7182" style="font-family: STIXGeneral-Italic;">w</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: 10.9px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-386">w</script>
 </li>
-<li>The attribute values match: <span class="MathJax_Preview">match(W,deriv,attrs)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-387-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-387-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7183"><span style="display: inline-block; position: relative; width: 167px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 54.4px -8.8px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7184"><span class="mi" id="MathJax-Span-7185" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7186" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7187" 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-7188" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7189" style="font-family: STIXGeneral-Italic;">h</span><span class="mo" id="MathJax-Span-7190" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7191" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7192" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7193" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7194" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7195" 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-7196" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7197" style="font-family: STIXGeneral-Italic;">v</span><span class="mo" id="MathJax-Span-7198" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7199" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7200" 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-7201" 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-7202" 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-7203" style="font-family: STIXGeneral-Italic;">s</span><span class="mo" id="MathJax-Span-7204" 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: 18.6px; vertical-align: -4.4px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-387">match(W,deriv,attrs)</script>.
 </li></ol></div>
 </section>
 </section>
@@ -1957,7 +1952,7 @@
 <section id="specialization">
 <h4><span class="secno">4.4.12 </span> Specialization </h4>
 
-<p>The <span class="MathJax_Preview">specializationOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-388-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-388-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7205"><span style="display: inline-block; position: relative; width: 181px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7206"><span class="mi" id="MathJax-Span-7207" style="font-family: STIXGeneral-Italic;">s</span><span class="mi" id="MathJax-Span-7208" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7209" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7210" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7211" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7212" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7213" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7214" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7215" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-7216" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7217" 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-7218" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7219" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7220" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7221" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7222" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7223" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7224"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7225" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7226" 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-7227" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7228" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7229" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7230" 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-7231" 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-388">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
@@ -1966,26 +1961,25 @@
     </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">W,\rho \models specializationOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-389-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-389">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
+  <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-389-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7232"><span style="display: inline-block; position: relative; width: 240px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7233"><span class="mi" id="MathJax-Span-7234" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7235" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7236" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7237" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7238" style="font-family: STIXGeneral-Italic; padding-left: 6px;">s</span><span class="mi" id="MathJax-Span-7239" style="font-family: STIXGeneral-Italic;">p</span><span class="mi" id="MathJax-Span-7240" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7241" style="font-family: STIXGeneral-Italic;">c</span><span class="mi" id="MathJax-Span-7242" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7243" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7244" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7245" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7246" style="font-family: STIXGeneral-Italic;">z</span><span class="mi" id="MathJax-Span-7247" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7248" 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-7249" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7250" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7251" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7252" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7253" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7254" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7255"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7256" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7257" 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-7258" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7259" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7260" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7261" 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-7262" 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-389">W,\rho \models specializationOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview">e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-390-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-390">e_1</script> and <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-391-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-391">e_2</script> are entity identifiers, denoting
-  distinct entities <span class="MathJax_Preview">ent_1
-  = \rho(e_1) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-392-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-392">ent_1
-  = \rho(e_1) \in Entities</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2) \in Entities</span><span class="MathJax MathJax_Processing" id="MathJax-Element-393-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-393">ent_2 = \rho(e_2) \in Entities</script>,
-  where <span class="MathJax_Preview">ent_1 \neq ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-394-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-394">ent_1 \neq ent_2</script>.
+<li>[WF] Both <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-390-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7263"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7264"><span class="msubsup" id="MathJax-Span-7265"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7266" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7267" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-390">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-391-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7268"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7269"><span class="msubsup" id="MathJax-Span-7270"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7271" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7272" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></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" id="MathJax-Element-392-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7273"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7274"><span class="mi" id="MathJax-Span-7275" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7276" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7277"><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-7278" 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-7279" 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-7280" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7281" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7282" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7283"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7284" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7285" 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-7286" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7287" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7288" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7289" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7290" 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-7291" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7292" 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-7293" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7294" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7295" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-393-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7296"><span style="display: inline-block; position: relative; width: 177px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7297"><span class="mi" id="MathJax-Span-7298" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7299" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7300"><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-7301" 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-7302" 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-7303" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7304" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7305" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7306"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7307" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7308" 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-7309" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7310" style="font-family: STIXGeneral-Regular; padding-left: 6px;">∈</span><span class="mi" id="MathJax-Span-7311" style="font-family: STIXGeneral-Italic; padding-left: 6px;">E<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mi" id="MathJax-Span-7312" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7313" 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-7314" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7315" 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-7316" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7317" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7318" style="font-family: STIXGeneral-Italic;">s</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: -5px;"></span></span></nobr></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" id="MathJax-Element-394-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7319"><span style="display: inline-block; position: relative; width: 92px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(32.2px 19360px 54px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7320"><span class="mi" id="MathJax-Span-7321" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7322" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7323"><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-7324" 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-7325" 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-7326" style="font-family: STIXGeneral-Regular; padding-left: 6px;">≠</span><span class="mi" id="MathJax-Span-7327" style="font-family: STIXGeneral-Italic; padding-left: 6px;">e</span><span class="mi" id="MathJax-Span-7328" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7329"><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-7330" 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-7331" 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><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: 17.8px; vertical-align: -4px;"></span></span></nobr></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">thingOf(ent_1) = thingOf(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-395-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-395">thingOf(ent_1) = thingOf(ent_2)</script>.
+<li>The two Entities refer to the same Thing, that is, <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-395-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7332"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7333"><span class="mi" id="MathJax-Span-7334" 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-7335" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7336" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7337" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7338" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7339" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7340" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7341" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7342" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7343" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7344"><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-7345" 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-7346" 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-7347" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7348" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7349" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7350" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7351" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7352" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7353" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7354" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7355" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7356" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7357" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7358" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7359"><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-7360" 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-7361" 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-7362" 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-395">thingOf(ent_1) = thingOf(ent_2)</script>.
 </li>
-<li>The lifetime of <span class="MathJax_Preview">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-396-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-396">obj_1</script> is contained in that of <span class="MathJax_Preview">ent_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-397-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-397">ent_2</script>, i.e. <span class="MathJax_Preview">lifetime(ent_1) \subseteq lifetime(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-398-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-398">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
+<li>The lifetime of <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-396-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7363"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7364"><span class="mi" id="MathJax-Span-7365" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7366" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7367"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7368" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7369" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-397-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7370"><span style="display: inline-block; position: relative; width: 33px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 53.9px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7371"><span class="mi" id="MathJax-Span-7372" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7373" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7374"><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-7375" 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-7376" 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><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: 15.5px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-397">ent_2</script>, i.e. <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-398-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7377"><span style="display: inline-block; position: relative; width: 230px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.2px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7378"><span class="mi" id="MathJax-Span-7379" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7380" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7381" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-7382" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7383" 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-7384" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7385" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7386" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7387" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7388" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7389" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7390"><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-7391" 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-7392" 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-7393" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7394" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊆</span><span class="mi" id="MathJax-Span-7395" style="font-family: STIXGeneral-Italic; padding-left: 6px;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7396" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7397" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mi" id="MathJax-Span-7398" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7399" 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-7400" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7401" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7402" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7403" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7404" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7405" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7406"><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-7407" 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-7408" 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-7409" 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-398">lifetime(ent_1) \subseteq lifetime(ent_2)</script>.
 </li>
-<li>For each attribute <span class="MathJax_Preview">attr</span><span class="MathJax MathJax_Processing" id="MathJax-Element-399-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-399">attr</script> we have <span class="MathJax_Preview">value(obj_1,attr) \supseteq value(obj_2,attr)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-400-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-400">value(obj_1,attr) \supseteq value(obj_2,attr)</script>.
+<li>For each attribute <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-399-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7410"><span style="display: inline-block; position: relative; width: 28px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(34.4px 19360px 51.2px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7411"><span class="mi" id="MathJax-Span-7412" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7413" 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-7414" 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-7415" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></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: 12.8px; vertical-align: -1.2px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-399">attr</script> we have <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-400-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7416"><span style="display: inline-block; position: relative; width: 270px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7417"><span class="mi" id="MathJax-Span-7418" style="font-family: STIXGeneral-Italic;">v</span><span class="mi" id="MathJax-Span-7419" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7420" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7421" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7422" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7423" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7424" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7425" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7426"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7427" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7428" 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-7429" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7430" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7431" 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-7432" 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-7433" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7434" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7435" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊇</span><span class="mi" id="MathJax-Span-7436" style="font-family: STIXGeneral-Italic; padding-left: 6px;">v</span><span class="mi" id="MathJax-Span-7437" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7438" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7439" style="font-family: STIXGeneral-Italic;">u</span><span class="mi" id="MathJax-Span-7440" style="font-family: STIXGeneral-Italic;">e</span><span class="mo" id="MathJax-Span-7441" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7442" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7443" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7444"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7445" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7446" 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-7447" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7448" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">a</span><span class="mi" id="MathJax-Span-7449" 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-7450" 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-7451" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7452" 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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-400">value(obj_1,attr) \supseteq value(obj_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">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-401-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-401">obj_1</script> and
-<span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-402-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-402">obj_2</script> to have the same lifetime (or that of <span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-403-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-403">obj_2</script> can be larger).
-The last criterion allows <span class="MathJax_Preview">obj_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-404-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-404">obj_1</script> to have more defined attributes than
-<span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-405-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-405">obj_2</script>, but they must include the attributes defined by <span class="MathJax_Preview">obj_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-406-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-406">obj_2</script>.
+the same Thing. Note that the third criterion allows <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-401-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7453"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7454"><span class="mi" id="MathJax-Span-7455" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7456" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7457"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7458" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7459" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-401">obj_1</script> and
+<span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-402-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7460"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7461"><span class="mi" id="MathJax-Span-7462" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7463" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7464"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7465" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7466" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-403-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7467"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7468"><span class="mi" id="MathJax-Span-7469" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7470" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7471"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7472" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7473" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-404-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7474"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7475"><span class="mi" id="MathJax-Span-7476" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7477" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7478"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7479" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7480" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-405-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7481"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7482"><span class="mi" id="MathJax-Span-7483" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7484" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7485"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7486" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7487" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></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" id="MathJax-Element-406-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7488"><span style="display: inline-block; position: relative; width: 34px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55.7px -8.5px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7489"><span class="mi" id="MathJax-Span-7490" style="font-family: STIXGeneral-Italic;">o</span><span class="mi" id="MathJax-Span-7491" style="font-family: STIXGeneral-Italic;">b</span><span class="msubsup" id="MathJax-Span-7492"><span style="display: inline-block; position: relative; width: 13.4px; height: 0px;"><span style="position: absolute; clip: rect(32.4px 19360px 55px -11.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7493" style="font-family: STIXGeneral-Italic;">j<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -37.3px; left: 5px;"><span class="mn" id="MathJax-Span-7494" 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><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: 19.9px; vertical-align: -5.7px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-406">obj_2</script>.
 </p>
 
 </section>
@@ -1993,15 +1987,15 @@
 
 <h4><span class="secno">4.4.13 </span> Alternate </h4>
 
-<p>The <span class="MathJax_Preview">alternateOf</span><span class="MathJax MathJax_Processing" id="MathJax-Element-407-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-407-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7495"><span style="display: inline-block; position: relative; width: 91px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.7px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7496"><span class="mi" id="MathJax-Span-7497" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7498" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7499" 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-7500" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7501" 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-7502" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7503" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7504" 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-7505" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7506" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7507" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></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-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>
 <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">W,\rho \models alternateOf(e_1,e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-408-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-408-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7508"><span style="display: inline-block; position: relative; width: 204px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7509"><span class="mi" id="MathJax-Span-7510" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7511" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7512" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7513" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7514" style="font-family: STIXGeneral-Italic; padding-left: 6px;">a</span><span class="mi" id="MathJax-Span-7515" style="font-family: STIXGeneral-Italic;">l<span style="display: inline-block; overflow: hidden; height: 1px; width: 0px;"></span></span><span class="mi" id="MathJax-Span-7516" 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-7517" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7518" 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-7519" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7520" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7521" 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-7522" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7523" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7524" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7525" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7526"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7527" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7528" 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-7529" style="font-family: STIXGeneral-Regular;">,</span><span class="msubsup" id="MathJax-Span-7530" style="padding-left: 3.6px;"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7531" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7532" 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-7533" 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-408">W,\rho \models alternateOf(e_1,e_2)</script> holds if and only if:</p>
 <ol>
-<li>[WF] Both <span class="MathJax_Preview">e_1</span><span class="MathJax MathJax_Processing" id="MathJax-Element-409-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-409">e_1</script> and <span class="MathJax_Preview">e_2</span><span class="MathJax MathJax_Processing" id="MathJax-Element-410-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-410">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview">ent_1 = \rho(e_1)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-411-Frame" role="textbox" aria-readonly="true"></span><script type="math/tex" id="MathJax-Element-411">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview">ent_2 = \rho(e_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-412-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-409-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7534"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7535"><span class="msubsup" id="MathJax-Span-7536"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7537" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7538" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-409">e_1</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-410-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7539"><span style="display: inline-block; position: relative; width: 17px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(29.5px 19360px 46.9px -8.4px); top: -41px; left: 0px;"><span class="mrow" id="MathJax-Span-7540"><span class="msubsup" id="MathJax-Span-7541"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7542" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7543" 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><span style="display: inline-block; width: 0px; height: 41px;"></span></span></span><span style="border-left-width: 0px; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 13.4px; vertical-align: -3.9px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-410">e_2</script> are entity identifiers, denoting <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-411-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7544"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7545"><span class="mi" id="MathJax-Span-7546" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7547" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7548"><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-7549" 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-7550" 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-7551" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7552" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7553" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7554"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7555" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7556" 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-7557" 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: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-411">ent_1 = \rho(e_1)</script> and <span class="MathJax_Preview"></span><span class="MathJax" id="MathJax-Element-412-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7558"><span style="display: inline-block; position: relative; width: 96px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.9px 19360px 55px -8.4px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7559"><span class="mi" id="MathJax-Span-7560" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7561" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7562"><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-7563" 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-7564" 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-7565" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7566" style="font-family: STIXGeneral-Italic; padding-left: 6px;">ρ</span><span class="mo" id="MathJax-Span-7567" style="font-family: STIXGeneral-Regular;">(</span><span class="msubsup" id="MathJax-Span-7568"><span style="display: inline-block; position: relative; width: 16.5px; height: 0px;"><span style="position: absolute; clip: rect(36.5px 19360px 51.2px -8.4px); top: -48px; left: 0px;"><span class="mi" id="MathJax-Span-7569" style="font-family: STIXGeneral-Italic;">e</span><span style="display: inline-block; width: 0px; height: 48px;"></span></span><span style="position: absolute; top: -39.1px; left: 8px;"><span class="mn" id="MathJax-Span-7570" 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-7571" 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: 19.1px; vertical-align: -5px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-412">ent_2 = \rho(e_2)</script>.
 </li>
-<li>The two objects refer to the same underlying Thing: <span class="MathJax_Preview">thingOf(ent_1) = thingOf(ent_2)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-413-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-413-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7572"><span style="display: inline-block; position: relative; width: 238px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -8.3px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7573"><span class="mi" id="MathJax-Span-7574" 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-7575" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7576" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7577" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7578" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7579" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7580" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7581" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7582" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7583" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7584"><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-7585" 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-7586" 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-7587" style="font-family: STIXGeneral-Regular;">)</span><span class="mo" id="MathJax-Span-7588" style="font-family: STIXGeneral-Regular; padding-left: 6px;">=</span><span class="mi" id="MathJax-Span-7589" style="font-family: STIXGeneral-Italic; padding-left: 6px;">t<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.3px;"></span></span><span class="mi" id="MathJax-Span-7590" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7591" style="font-family: STIXGeneral-Italic;">i</span><span class="mi" id="MathJax-Span-7592" style="font-family: STIXGeneral-Italic;">n</span><span class="mi" id="MathJax-Span-7593" style="font-family: STIXGeneral-Italic;">g</span><span class="mi" id="MathJax-Span-7594" style="font-family: STIXGeneral-Italic;">O</span><span class="mi" id="MathJax-Span-7595" style="font-family: STIXGeneral-Italic;">f<span style="display: inline-block; overflow: hidden; height: 1px; width: 2.8px;"></span></span><span class="mo" id="MathJax-Span-7596" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7597" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7598" style="font-family: STIXGeneral-Italic;">n</span><span class="msubsup" id="MathJax-Span-7599"><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-7600" 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-7601" 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-7602" 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-413">thingOf(ent_1) = thingOf(ent_2)</script>
 </li></ol>
 </div>
 
@@ -2013,15 +2007,14 @@
 
 <h4><span class="secno">4.4.14 </span> Membership </h4>
 
-<p>The <span class="MathJax_Preview">hadMember</span><span class="MathJax MathJax_Processing" id="MathJax-Element-414-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-414-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7603"><span style="display: inline-block; position: relative; width: 95px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 51.3px -8.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7604"><span class="mi" id="MathJax-Span-7605" style="font-family: STIXGeneral-Italic;">h</span><span class="mi" id="MathJax-Span-7606" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7607" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7608" style="font-family: STIXGeneral-Italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-7609" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7610" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7611" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-7612" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7613" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></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: 15.5px; vertical-align: -1.3px;"></span></span></nobr></span><script type="math/tex" id="MathJax-Element-414">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>
   <p>
-  <span class="MathJax_Preview">W,\rho \models hadMember(c,e)</span><span class="MathJax MathJax_Processing" id="MathJax-Element-415-Frame" role="textbox" aria-readonly="true"></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" id="MathJax-Element-415-Frame" role="textbox" aria-readonly="true" style=""><nobr><span class="math" id="MathJax-Span-7614"><span style="display: inline-block; position: relative; width: 191px; height: 0px; font-size: 121%;"><span style="position: absolute; clip: rect(31.8px 19360px 55px -7.6px); top: -48px; left: 0px;"><span class="mrow" id="MathJax-Span-7615"><span class="mi" id="MathJax-Span-7616" style="font-family: STIXGeneral-Italic;">W<span style="display: inline-block; overflow: hidden; height: 1px; width: 1.4px;"></span></span><span class="mo" id="MathJax-Span-7617" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7618" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">ρ</span><span class="mo" id="MathJax-Span-7619" style="font-family: STIXGeneral-Regular; padding-left: 6px;">⊨</span><span class="mi" id="MathJax-Span-7620" style="font-family: STIXGeneral-Italic; padding-left: 6px;">h</span><span class="mi" id="MathJax-Span-7621" style="font-family: STIXGeneral-Italic;">a</span><span class="mi" id="MathJax-Span-7622" style="font-family: STIXGeneral-Italic;">d<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.5px;"></span></span><span class="mi" id="MathJax-Span-7623" style="font-family: STIXGeneral-Italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.8px;"></span></span><span class="mi" id="MathJax-Span-7624" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7625" style="font-family: STIXGeneral-Italic;">m</span><span class="mi" id="MathJax-Span-7626" style="font-family: STIXGeneral-Italic;">b</span><span class="mi" id="MathJax-Span-7627" style="font-family: STIXGeneral-Italic;">e</span><span class="mi" id="MathJax-Span-7628" style="font-family: STIXGeneral-Italic;">r<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.4px;"></span></span><span class="mo" id="MathJax-Span-7629" style="font-family: STIXGeneral-Regular;">(</span><span class="mi" id="MathJax-Span-7630" style="font-family: STIXGeneral-Italic;">c</span><span class="mo" id="MathJax-Span-7631" style="font-family: STIXGeneral-Regular;">,</span><span class="mi" id="MathJax-Span-7632" style="font-family: STIXGeneral-Italic; padding-left: 3.6px;">e</span><span class="mo" id="MathJax-Span-7633" style="font-family: STIXGeneral-Regular;">)</span></span><span style="display: inline-block; width: 0px; height: 48px;"></span></span></span><span styl