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Fixes correctness of Appendix A (from issue #139) #160

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Fixes correctness of Appendix A (from issue #139) #160

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92f2a8d
Fixes correctness of Appendix A (from issue #139)
franconi Oct 2, 2025
09f18ce
fix problems in entailment closure
pfps Oct 8, 2025
5340b59
Merge pull request #1 from franconi/peter
franconi Oct 9, 2025
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57 changes: 28 additions & 29 deletions spec/index.html
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Original file line number Diff line number Diff line change
Expand Up @@ -1814,10 +1814,33 @@ <h2>Entailment rules</h2>
<p><code>ex:a rdfs:subPropertyOf _:b .<br/>
_:b rdfs:domain ex:c .<br/>
ex:d ex:a ex:e .<br/>
ex:d _:b ex:c .</code> by <a>rdfs7</a><br/>
ex:d _:b ex:e .</code> by <a>rdfs7</a><br/>
<code>ex:d rdf:type ex:c .</code> by <a>rdfs2</a></p>

<p>Where the entailment patterns have been applied to generalized RDF syntax but yield a final conclusion which is legal RDF.</p>

<p>
The entailment pattern for generalized RDF with [=symmetric RDF triples=],
considering that, according to the semantics, the denotation of triple terms should
be of type <code>rdfs:Proposition</code>, is the following:
</p>
<table>
<caption>RDFS-T entailment pattern.</caption>
<tbody>
<tr>
<th > </th>
<th ><strong>any S</strong></th>
<th ><strong>then S RDFS entails</strong></th>
</tr>
<tr >
<td class="othertable"><dfn>Grdfs14</dfn></td>
<td class="othertable">if S contains <code>yyy rdf:type rdf:Property .</code><br/>
and <code>xxx</code> and <code>yyy</code> appear in E
</td>
<td class="othertable"><code>&lt;&lt;(xxx yyy zzz)>> rdf:type rdfs:Proposition .</code></td>
</tr>
</tbody>
</table>

<p>With the generalized syntax, these rules are postulated to be complete for both RDF and RDFS entailment. Stated exactly:</p>

Expand All @@ -1828,8 +1851,8 @@ <h2>Entailment rules</h2>
<li>Add to S all the RDF (and RDFS) axiomatic triples which do not contain any container membership property IRI.</li>
<li>For each container membership property IRI which occurs in E, add the RDF (and RDFS) axiomatic triples which contain that IRI.</li>
<li>If no triples were added in step 2, add the RDF (and RDFS) axiomatic triples which contain <code>rdf:_1</code>.</li>
<li>For every IRI or literal <code>aaa</code> used in E, add <code>aaa rdf:type rdfs:Resource</code> to S.</li>
<li>Apply the rules <a>GrdfD1</a>, <a>rdfD1a</a>, and <a>rdfD2</a> (and the rules <a>rdfs1</a> through <a>rdfs13</a>),
<li>Apply the rule GrdfD1 (and rdfs1 and rdfs4) but using E instead of S in the antecedent.</li>
<li>Apply the rules <a>GrdfD1</a>, <a>rdfD1a</a>, and <a>rdfD2</a> (and the rules <a>rdfs1</a> through <a>rdfs13</a> and <a>Grdfs14</a>),
with D={<code>rdf:langString</code>, <code>rdf:dirLangString</code>, <code>xsd:string</code>},
to the set in all possible ways, to exhaustion.</li>
</ol>
Expand All @@ -1843,9 +1866,9 @@ <h2>Entailment rules</h2>
Detecting simple entailment is NP-complete in general, but of low polynomial order when E contains no blank nodes.</p>

<p>Every RDF(S) closure, even starting with the empty graph,
will contain all RDF(S) tautologies which can be expressed using the vocabulary of the original graph
will contain all RDF(S) tautologies which can be expressed using the vocabulary of the entailing and entailed graphs
plus the RDF and RDFS vocabularies.
In practice there is little utility in re-deriving these,
In practice there is little utility in re-deriving these
and a subset of the rules can be used to establish most entailments of practical interest.</p>

<p>If it is important to stay within legal RDF syntax, rule <a>rdfD1</a> may be used instead of <a>GrdfD1</a>,
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<p>If it is important to stay within legal RDF syntax, rule <a>rdfD1</a> may be used instead of <a>GrdfD1</a>,
<p>If it is important to stay within legal RDF syntax, rule <a>rdfD1</a> may be used instead of <a>GrdfD1</a> and <a>rdfs14</a> instead of <a>Grdfs14</a>,

Expand All @@ -1855,30 +1878,6 @@ <h2>Entailment rules</h2>
<p>As noted earlier, detecting datatype entailment for larger sets of datatype IRIs
requires attention to idiosyncratic properties of the particular datatypes.</p>

<p>
The entailment pattern for generalized RDF with [=symmetric RDF triples=],
considering that, according to the semantics, the denotation of triple terms should
be of type <code>rdfs:Proposition</code>, is the following:
</p>
<table>
<caption>RDFS-T entailment pattern.</caption>
<tbody>
<tr>
<th > </th>
<th ><strong>if S contains</strong></th>
<th ><strong>then S RDFS entails</strong></th>
</tr>
<tr >
<td class="othertable"><dfn>Grdfs14</dfn></td>
<td class="othertable">xxx <code>rdf:type rdfs:Resource .</code><br/>
yyy <code>rdf:type rdf:Property .</code><br/>
zzz <code>rdf:type rdfs:Resource .</code><br/>
</td>
<td class="othertable"><code>&lt;&lt;(xxx yyy zzz)>> rdf:type rdfs:Proposition .</code></td>
</tr>
</tbody>
</table>


</section>

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