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Remove Appendix B #161

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Removed Appendix B
franconi Oct 7, 2025
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reference to finite interpretation from RDF 1.1
franconi Oct 7, 2025
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Better text
franconi Oct 8, 2025
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48 changes: 5 additions & 43 deletions spec/index.html
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Expand Up @@ -436,10 +436,11 @@ <h2>Simple Interpretations</h2>

<p class="technote">Simple interpretations are required to interpret all <a>names</a>,
and are therefore infinite.
This simplifies the exposition.
However, RDF can be interpreted using finite structures,
supporting decidable algorithms.
Details are given in <a href="#finite_interpretations" class="sectionRef"></a>. </p>
It was shown in
<a href="https://www.w3.org/TR/rdf11-mt/#finite-interpretations-informative">Appendix B</a>
of RDF 1.1 Semantics spec.
that RDF 1.1 could be interpreted using finite structures.
</p>

<p>IEXT(x), called the <dfn class="no-export lint-ignore">extension</dfn> of x,
is a set of pairs which identify the arguments for which the property is true,
Expand Down Expand Up @@ -1882,45 +1883,6 @@ <h2>Entailment rules</h2>

</section>

<section id="finite_interpretations" class="informative appendix">
<h2>Finite interpretations</h2>

<p>To keep the exposition simple, the RDF semantics has been phrased in a way which requires interpretations
to be larger than absolutely necessary.
For example, all interpretations are required to interpret the whole IRI vocabulary,
and the universes of all D-interpretations where D contains
<code>xsd:string</code> must contain all possible strings and therefore be infinite.
This appendix sketches, without proof, how to re-state the semantics using smaller semantic structures
without changing any entailments. </p>

<p>Basically, it is only necessary for an interpretation structure to interpret the <a>names</a>
actually used in the graphs whose entailment is being considered, and to consider interpretations
whose universes are at most as big as the number of <a>name</a>s and blank nodes in the graphs.
More formally, we can define a <dfn>pre-interpretation</dfn> over a <a>vocabulary</a> V to be a structure I
similar to a <a>simple interpretation</a> but with a mapping only from V to its universe IR.
Then when determining whether G entails E, consider only pre-interpretations over the finite vocabulary
of <a>names</a> actually used in G union E. The universe of such a pre-interpretation can be restricted to the cardinality N+B+1, where N is the size of the vocabulary and B is the number of blank nodes in the graphs. Any such pre-interpretation may be extended to <a>simple interpretation</a>s, all of which will give the same truth values for any triples in G or E. Satisfiability, entailment and so on can then be defined with respect to these finite pre-interpretations, and shown to be identical to the ideas defined in the body of the specification.</p>

<p>When considering D-entailment, <a>pre-interpretation</a>s may be kept finite
by weakening the semantic conditions for literals so that IR needs to contain literal values
only for literals which actually occur in G or E, and the size of the universe restricted to (N+B)×(D+1),
where D is the number of recognized datatypes.
(A tighter bound is possible.) For RDF entailment,
only the finite part of the RDF vocabulary which includes those container membership properties
which actually occur in the graphs need to be interpreted,
and the second RDF semantic condition is weakened to apply only to values
which are values of literals which actually occur in the vocabulary.
For RDFS interpretations, again only that finite part of the infinite container membership property vocabulary
which actually occurs in the graphs under consideration needs to be interpreted.
In all these cases, a <a>pre-interpretation</a> of the vocabulary of a graph may be extended to a full interpretation
of the appropriate type without changing the truth-values of any triples in the graphs.</p>

<p>The whole semantics could be stated in terms of <a>pre-interpretation</a>s,
yielding the same entailments, and allowing finite RDF graphs to be interpreted in finite structures,
if the <em>finite model property</em> is considered important.</p>

</section>

<section id="proofs" class="informative appendix">
<h2>Proofs of some results</h2>

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