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Details are given in <ahref="#finite_interpretations" class="sectionRef"></a>. </p>
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<p>IEXT(x), called the <dfnclass="export">extension</dfn> of x,
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<p>IEXT(x), called the <dfnclass="no-export lint-ignore">extension</dfn> of x,
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is a set of pairs which identify the arguments for which the property is true,
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that is, a binary relational extension.</p>
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@@ -562,9 +563,9 @@ <h2>Simple Entailment</h2>
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E when I(E)=true, that E is (simply) <dfn>satisfiable</dfn>
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when a simple interpretation exists which <a>satisfies</a> it,
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otherwise (simply) <dfn>unsatisfiable</dfn>,
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and that a graph G simply <dfndata-lt="entail" data-local-lt="simple entailment|entailment">entails</dfn>
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and that a graph G simply <dfnid="dfn-entail" data-cite="RDF12-CONCEPTS#dfn-entailment" data-lt="entail" data-local-lt="simple entailment|entailment">entails</dfn>
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a graph E when every interpretation which <a>satisfies</a> G also satisfies E.
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If two graphs E and F each entail the other then they are logically <dfn>equivalent</dfn>.</p>
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If two graphs E and F each entail the other then they are logically <dfnid="dfn-equivalent" data-cite="RDF12-CONCEPTS#dfn-equivalence">equivalent</dfn>.</p>
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<p>In later sections these notions will be adapted to other classes of interpretations,
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but throughout this section 'entailment' should be interpreted as meaning simple entailment.</p>
@@ -581,7 +582,7 @@ <h2>Simple Entailment</h2>
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<p>Any process which constructs a graph E from
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some other graph S is (simply) <dfn>valid</dfn> if S
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<a>simply entails</a> E in every case,
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otherwise <dfnclass="export">invalid</dfn><spanid="dfn-invalid.x"><!-- obsolete term --></span>.</p>
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otherwise <dfnclass="no-export lint-ignore">invalid</dfn><spanid="dfn-invalid.x"><!-- obsolete term --></span>.</p>
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<p>The fact that an inference is valid should not be understood as meaning
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that any RDF application is obliged or required to make the inference.
@@ -682,7 +683,7 @@ <h3>Properties of simple entailment (Informative)</h3>
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<sectionid="skolemization" class="informative">
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<h2>Skolemization (Informative)</h2>
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<p><dfnclass="export">Skolemization</dfn> is a transformation on RDF graphs
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<p><dfnclass="no-export lint-ignore">Skolemization</dfn> is a transformation on RDF graphs
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which eliminates blank nodes by replacing them with "new" IRIs,
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which means IRIs which are coined for this purpose and are therefore guaranteed
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to not occur in any other RDF graph (at the time of creation).
@@ -842,15 +843,15 @@ <h2>D-interpretations</h2>
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<sectionid="D_entailment">
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<h3>Datatype entailment</h3>
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<p>A graph is (simply) <dfnclass="export">D-satisfiable</dfn> or
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<dfnclass="export">satisfiable recognizing D</dfn> when it has the value true
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<p>A graph is (simply) <dfnclass="no-export lint-ignore">D-satisfiable</dfn> or
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<dfnclass="no-export lint-ignore">satisfiable recognizing D</dfn> when it has the value true
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in some D-interpretation, and a graph S (simply) <dfn>D-entails</dfn> or
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<dfn>entails recognizing D</dfn> a graph G when every D-interpretation which
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<a>satisfies</a> S also D-satisfies G.</p>
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<p> Unlike the case with <a>simple interpretation</a>s,
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it is possible for a graph to have no satisfying D-interpretations
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i.e. to be <dfndata-lt="D-unsatisfiability">D-unsatisfiable</dfn>.
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i.e. to be <dfnclass="no-export lint-ignore" data-lt="D-unsatisfiability">D-unsatisfiable</dfn>.
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RDF processors MAY treat an unsatisfiable graph as signaling an error condition,
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but this is not required.</p>
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@@ -1341,78 +1342,78 @@ <h4>Patterns of RDFS entailment (Informative)</h4>
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<th>then S RDFS <a>entails recognizing D</a>:</th>
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