author | Peter F. Patel-Schneider <pfpschneider@gmail.com> |

Wed, 03 Jul 2013 09:43:23 -0700 | |

changeset 911 | eb3cce7b99f1 |

parent 908 | 95838b4373d6 |

child 912 | ca3dd1c28a69 |

more html fixes for LC

rdf-mt/index.html |

--- a/rdf-mt/index.html Wed Jul 03 12:37:23 2013 -0400 +++ b/rdf-mt/index.html Wed Jul 03 09:43:23 2013 -0700 @@ -1079,7 +1079,7 @@ <h2 id="appendices">Appendices</h2> -<section class="appendix,informative"><h2 id="entailment_rules">Entailment rules (Informative)</h2> +<section class="informative"><h2 id="entailment_rules">Entailment rules (Informative)</h2> <p>(<em>This section is based on work described more fully in </em>[[HORST04]]<em>, </em>[[HORST05]]<em>, which should be consulted for technical details and proofs.</em>) </p> <p> The RDF and RDFS entailment patterns listed in the above tables can be viewed as left-to-right rules which add the entailed conclusion to a graph. These rule sets can be used to check RDF (or RDFS) entailment between graphs S and E, by the following sequence of operations:</p> @@ -1180,7 +1180,7 @@ </section> -<section class="appendix" class="informative"><h2 id="finite_interpretations">Finite interpretations (Informative)</h2> +<section class="informative"><h2 id="finite_interpretations">Finite interpretations (Informative)</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 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>name</a>s 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 names 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>name</a>s 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 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> @@ -1192,7 +1192,7 @@ </section> -<section class="appendix" class="informative"><h2 id="proofs">Proofs of some results (Informative)</h2> +<section class="informative"><h2 id="proofs">Proofs of some results (Informative)</h2> <p class="fact"> The <a>empty graph</a> is entailed by any graph, and does not entail any graph except itself. @@ -1237,7 +1237,7 @@ </section> -<section class="appendix" class="informative" id="whatnot"><h2 id="non_semantics">RDF reification, containers and collections (Informative)</h2> +<section class="informative" id="whatnot"><h2 id="non_semantics">RDF reification, containers and collections (Informative)</h2> <p>The RDF semantic conditions do not place formal constraints on the meaning of much of the RDF vocabulary which is intended for use in describing containers and bounded collections, @@ -1512,7 +1512,7 @@ </section> - <section class='appendix' class="informative"> + <section class="informative"> <h2 id="acknowledgements">Acknowledgements</h2> <p>The basic idea of using an explicit extension mapping to allow self-application without violating the axiom of foundation was