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<p>A <dfn>simple interpretation</dfn> I is a structure consisting of:</p>
<div class="tabletitle">Definition of a simple interpretation.</div>
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<td class="semantictable">1. A non-empty set IR of resources, called the domain or universe
of I.
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<div class="tabletitle">Semantic conditions for ground graphs.</div>
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<p> Suppose I is a simple interpretation and A is a mapping from a set of blank nodes to the universe IR of I. Define the mapping [I+A] to be I on <a>name</a>s, and A on blank nodes on the set: [I+A](x)=I(x) when x is a <a>name</a> and [I+A](x)=A(x) when x is a blank node; and extend this mapping to triples and RDF graphs using the rules given above for ground graphs. Then the semantic conditions for an RDF graph are:</p>
<div class="tabletitle">Semantic condition for blank nodes.</div>
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<p>Let D be a set of IRIs <a>identify</a>ing datatypes. A <strong>(simple)</strong> <dfn>D-interpretation</dfn> is a <a>simple interpretation</a> which satisfies the following conditions:</p>
<div class="tabletitle">Semantic conditions for datatyped literals.</div>
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<tr><td class="semantictable">If <code>rdf:langString</code> is in D, then for every language-tagged string E with lexical form sss and language tag ttt, IL(E)= < sss, ttt' >, where ttt' is ttt converted to lower case using US-ASCII rules </td></tr>
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set of IRIs with the namespace prefix <code>rdf:</code> .
<div >
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<td ><dfn>RDF vocabulary</dfn></td>
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<p>An <dfn>RDF interpretation</dfn> <strong>recognizing D</strong> is a <a>D-interpretation</a> I where D includes <code>rdf:langString</code> and <code>xsd:string</code>, and which satisfies:</p>
<div class="tabletitle">RDF semantic conditions.</div>
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<td class="semantictable" id="rdfsemcond1">x is
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<p>and satisfies every triple in the following infinite set:</p>
<div class="tabletitle">RDF axioms.</div>
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<td class="ruletable" id="RDF_axiomatic_triples"><code>rdf:type rdf:type rdf:Property .<br/>
rdf:subject rdf:type rdf:Property .<br/>
@@ -665,7 +667,7 @@
<p> The last semantic condition in the above table gives the following entailment pattern for <a>recognize</a>d datatype IRIs: </p>
<div class="tabletitle">RDF entailment pattern.</div>
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<th > </th>
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<p>In addition, the first RDF semantic condition justifies the following entailment pattern:</p>
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with more complex semantic constraints:</p>
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<td ><dfn>RDFS vocabulary</dfn></td>
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which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples. </p>
<div class="tabletitle">RDFS semantic conditions.</div>
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<td class="semantictable" id="rdfssemcond1"> <p>ICEXT(y) is defined to be { x : < x,y > is in IEXT(I(<code>rdf:type</code>)) }</p>
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<p>
</p>
<div class="tabletitle">RDFS axiomatic triples.</div>
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<p> Other triples which must be true in all RDFS interpretations
include the following. This is not a complete set.</p>
<div class="tabletitle">Some rdfs-valid triples.</div>
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<td class="ruletable"><code>rdfs:Resource rdf:type rdfs:Class .<br/>
rdfs:Class rdf:type rdfs:Class .<br/>
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<P>RDFS entailment holds for all the following patterns, which correspond closely to the RDFS semantic conditions:</p>
<div class="title">RDFS entailment patterns.</div>
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<p>This process is clearly correct, in that if it gives a positive result then indeed S does RDF (RDFS) entail E. It is not, however, complete: there are cases of S entailing E which are not detectable by this process. Examples include:</p>
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<p>Consider <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a> instead of RDF triples, graphs and datasets (extending the generalization used in [[HORST04]] and following exactly the terms used in [[OWL2-PROFILES]]). The semantics described in this document applies to the generalization without change, so that the notions of interpretation, satisfiability and entailment can be used freely. Then we can replace the first RDF entailment pattern with the simpler and more direct</p>
<div class="tabletitle">G-RDF-D entailment pattern.</div>
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<h3 id="Reif">Reification</h3>
<div class="c1">
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<td class="othertable"><strong>RDF reification vocabulary</strong></td>
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<h4 id="containers">RDF containers</h4>
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<td class="othertable"><strong>RDF(S) Container Vocabulary</strong></td>
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<h4 id="collections">RDF collections</h4>
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<td class="othertable"><strong>RDF Collection Vocabulary</strong></td>