--- a/rdf-mt/index.html Wed Apr 03 10:47:48 2013 -0700
+++ b/rdf-mt/index.html Wed Apr 03 11:01:20 2013 -0700
@@ -98,18 +98,18 @@
[[RDF-MT]] and supersedes that document.</p>
</section>
- <section class='introductory'><h2>Notes</h2>
+ <section class='introductory'><h2 id="notes">Notes</h2>
<p class='changenote'>Notes in this style indicate changes from the 2004 RDF semantics.</p>
<p class='technote'>Notes in this style are technical asides on obscure or recondite matters.</p></section>
<section>
- <h2>Introduction</h2>
+ <h2 id="introduction">Introduction</h2>
<p>
This document defines a model-theoretic semantics for RDF graphs and the RDF and RDFS vocabularies, providing an exact formal specification of when truth is preserved by transformations of RDF, or operations which derive RDF content from other RDF. Readers who are unfamiliar with model theory can find a brief introduction to the basic ideas and terminology in <a>Appendix A</a>, and may find the informative section 13 useful. </p>
<p>This specification is normative for RDF <a>formal</a> semantics. However, there are many aspects of RDF meaning which are not covered by this semantics, including social issues of how IRIs are assigned meanings in use, and how the referents of IRIs are related to Web content expressed in other media such as natural language texts. Accounts of such extended notions of meaning will go beyond this specification, but MUST NOT violate the conditions described here. </p>
</section>
<section>
- <h2>Semantic extensions and entailment regimes</h2>
+ <h2 id="extensions">Semantic extensions and entailment regimes</h2>
<p>RDF is intended for use as a base notation for a variety of extended notations such as OWL [[OWL2-OVERVIEW]] and RIF [[RIF-OVERVIEW]], whose expressions can be encoded as RDF graphs which use a particular vocabulary with a specially defined meaning. Also, particular IRI vocabularies may impose user-defined meanings upon the basic RDF meaning rules. When such extra meanings are assumed, a given RDF graph may support more extensive entailments than are sanctioned by the basic RDF semantics. In general, the more assumptions that are made about the meanings of IRIs in an RDF graph, the more valid entailments it has. </p>
<p>A particular such set of semantic assumptions is called a <dfn>semantic extension</dfn>. Each semantic extension defines an <dfn>entailment regime</dfn> of entailments which are valid under that extension. RDFS, described later in this document, is one such semantic extension. We will refer to an entailment regime by names such as <em>rdfs-entailment</em>, <em>D-entailment</em>, etc.. </p>
@@ -122,7 +122,7 @@
</section>
<section>
- <h2>Notation and terminology</h2>
+ <h2 id="notation">Notation and terminology</h2>
<p class="issue">This section needs cleaning up. Some of the 2004 definitions may no longer be needed. The notions of instance and equivalence may (?) need to be stated more carefully taking bnode scopes into account. Instance mappings should be defined on a whole scope rather than a graph (?). The definitions involving bnode scopes and complete graphs are new. <br/><br/> Maybe some of the material should be in Concepts. </p>
@@ -224,7 +224,7 @@
</section>
<section>
- <h2> Simple Interpretations</h2>
+ <h2 id="simple"> Simple Interpretations</h2>
<p>A <dfn>simple interpretation</dfn> I is a structure consisting of:</p>
@@ -298,7 +298,7 @@
<p>The sets IP and IR may overlap, indeed IP can be a subset of IR. Because of the domain conditions on IEXT, the denotation of the subject and object of any true triple will be in IR; so any IRI which occurs in a graph both as a predicate and as a subject or object will denote something in the intersection of IP and IR.</p>
- <h3>Blank Nodes</h3>
+ <h3 id="blank_nodes">Blank Nodes</h3>
<p>Blank nodes are treated as simply indicating the existence of a thing, without using an IRI to identify any particular thing. They play a similar role to existentially quantified variables in a conventional logical notation. This is not the same as assuming that the blank node indicates an 'unknown' IRI.
@@ -321,7 +321,7 @@
<p>Mappings from blank nodes to referents are not part of the definition of an interpretation, since the truth condition refers only to <em>some</em> such mapping. Blank nodes themselves differ from other nodes in not being assigned a denotation by an interpretation, reflecting the intuition that they have no 'global' meaning outside the scope in which they occur.</p>
-<h3>Intuitive summary</h3>
+<h3 id="intuitions">Intuitive summary</h3>
<p>An RDF graph is true exactly when:</p>
<p>1. the IRIs and literals in subject or object position in the graph all refer to things,</p><p>2. there is some way to interpret all the blank nodes in the scope as referring to things,</p><p>3. the IRIs in property position identify binary relationships,</p><p>4. and, under these interpretations, each triple S P O in the graph asserts that the thing referred to as S, and the thing referred to as O, do in fact stand in the relationship identified by P. </p>
@@ -346,7 +346,7 @@
<p>Entailment refers only to the truth of RDF graphs, not to their suitability for any other purpose. It is possible for an RDF graph to be fitted for a given purpose and yet validly entail another graph which is not appropriate for the same purpose. An example is the RDF test cases manifest [[!RDF-TESTCASES]] which is provided as an RDF document for user convenience. This document lists examples of correct entailments by describing their antecedents and conclusions. Considered as an RDF graph, the manifest validly entails a subgraph which omits the antecedents, and would therefore be incorrect if used as a test case manifest. This is not a violation of the RDF semantic rules, but it shows that the property of <em> "being a correct RDF test case manifest"</em> is not preserved under RDF entailment, and therefore cannot be described as an RDF semantic extension. Such entailment-risky uses of RDF should be restricted to cases, as here, where it is obvious to all parties what the intended special restrictions on entailment are, in contrast with the more normal case of using RDF for the open publication of data on the Web.</p>
-<h3>Some basic properties of simple entailment. </h3>
+<h3 id="basic_properties">Some basic properties of simple entailment. </h3>
<p>The properties described here apply only to simple entailment, not to extended notions
of entailment introduced in later sections. Proofs
are given in <a>Appendix B</a>.</p>
@@ -421,7 +421,7 @@
</section>
-<section><h2>Skolemization</h2>
+<section><h2 id="skolemization">Skolemization</h2>
<p>Skolemization is a transformation on RDF graphs which eliminates blank nodes by replacing them with "new" IRIs, which means IRIs which are coined for this purpose and are therefore guaranteed to not occur in any other RDF graph (at the time of creation). See ///Concepts#/// for a fuller discussion. </p>
<p> Suppose G is a graph containing blank nodes and sk is a skolemization mapping on the blank nodes in G, so that sk(G) is a skolemization of G. Then the semantic relationship between them can be summarized as follows. </p>
@@ -445,7 +445,7 @@
</section>
-<section><h2>Literals and datatypes</h2>
+<section><h2 id="datatypes">Literals and datatypes</h2>
<ul><li><p class="changenote"> In the 2004 RDF 1.0 specification, datatype D-entailment was defined as a semantic extension of RDFS-entailment. Here it is defined as a direct extension to basic RDF. This is more in conformity with actual usage, where RDF with datatypes is widely used without the RDFS vocabulary. If there is a need to distinguish this from the 2004 RDF 1.0 terminology, the longer phrasing "simple D-entailment" or "simple datatype entailment" should be used rather than "D-entailment". </p>
</li></ul>
@@ -463,7 +463,7 @@
</section>
-<section id="D_entailment"><h2>D-interpretations and datatype entailment</h2>
+<section id="D_interpretations"><h2>D-interpretations and datatype entailment</h2>
<p>Let D be a set of IRIs identifying datatypes. A <dfn>(simple) D-interpretation</dfn> is a simple interpretation which satisfies the following conditions:</p>
<div class="tabletitle">Semantic conditions for datatyped literals.</div>
@@ -481,7 +481,7 @@
<p></p>
</li></ul>
-<h3>Datatype entailment</h3>
+<h3 id="D-entailment">Datatype entailment</h3>
<p>A graph is (simply) <dfn>D-satisfiable</dfn> when it has the value true in some D-interpretation, and a set S of graphs (simply) <dfn>D-entails</dfn> a graph G when every D-interpretation which makes S true also D-satisfies G.</p>
@@ -503,7 +503,7 @@
</section>
-<section><h2>RDF-D Interpretations and RDF entailment</h2>
+<section><h2 id="rdf_d_interpretations">RDF-D Interpretations and RDF entailment</h2>
<p >RDF-D interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
set of IRIs in the <code>rdf:</code> namespace.
@@ -565,7 +565,7 @@
<code>aaa ppp _:x . <br/> _:x rdf:type xsd:integer .</code>
</section>
-<section><h2>RDFS Interpretations and RDFS entailment</h2>
+<section><h2 id="rdfs_interpretaitons">RDFS Interpretations and RDFS entailment</h2>
<p>RDF Schema [[RDF-SCHEMA]]
extends RDF to a larger <a id="defRDFSV"></a>vocabulary
with more complex semantic constraints:</p>
@@ -789,7 +789,7 @@
<p>RDFS does not partition the universe into disjoint categories of classes, properties and individuals. Anything in the universe can be used as a class or as a property, or both, while retaining its status as an individual which may be in classes and have properties. Thus, RDFS permits classes which contain other classes, classes of properties, properties of classes, etc. . As the axiomatic triples above illustrate, it also permits classes which contain themselves and properties which apply to themselves. A property of a class is not necessarily a property of its members, nor vice versa. </p>
-<h3>A note on rdfs:Literal</h3>
+<h3 id="rdfs_literal">A note on rdfs:Literal</h3>
<p>The class <code>rdfs:Literal</code> is not the class of literals, but rather that of literal <em>values</em>. For example, LV does not contain the literal <code>"24"^^xsd:integer</code> (although it might contain the string '<code>"24"^^http://www.w3.org/2001/XMLSchema#integer</code>' ) but it does contain the number twenty-four.</p>
<p>A triple of the form</p>
@@ -800,7 +800,7 @@
than a literal. It says that the IRI '<code>ex:a</code>'
refers to a literal value, which is quite possible since literal values are things in the universe. Similarly, blank nodes may range over literal values. </p>
-<h3>RDFS Entailment</h3>
+<h3 id="rdfs_entailment">RDFS Entailment</h3>
<p>S <i>rdfs-D-entails</i> E when every <a href="#rdfsinterpdef" class="termref">rdfs-D-interpretation</a>
which satisfies every member of S also satisfies E. RDFS entailment is rdfs-{<code>rdf:langString</code>, <code>xsd:string</code> }-entailment, i.e. rdfs-D-entailment with a minimal D. </p>
<p> Since every <a href="#rdfsinterpdef" class="termref">rdfs-D-interpretation</a> is an <a href="#rdfinterpdef" class="termref">rdf-D-interpretation</a>, if S rdfs-D-entails
@@ -814,7 +814,7 @@
</section>
-<section><h2>Monotonicity of semantic extensions </h2>
+<section><h2 id="monotonicity">Monotonicity of semantic extensions </h2>
<p>Given a set of RDF graphs, there are various ways in which one can 'add' information
to it. Any of the graphs may have some triples added to it; the set of graphs
may be extended by extra graphs; or the vocabulary of the graph may be interpreted
@@ -838,7 +838,7 @@
</section>
-<section class="informative"><h2>Extensional RDFS Semantic Conditions (Informative)</h2>
+<section class="informative"><h2 id="extensional_rdfs">Extensional RDFS Semantic Conditions (Informative)</h2>
<p class="issue">Is this section useful, or is it more likely to be confusing? Editor is inclined to delete it. </p>
<p>The semantics given above is deliberately chosen to be the weakest 'reasonable'
interpretation of the RDFS vocabulary. Semantic extensions MAY
@@ -880,22 +880,22 @@
</section>
-<section class="informative"><h2>Entailment Rules (Informative)</h2>
+<section class="informative"><h2 id="entailment_rules">Entailment Rules (Informative)</h2>
<p class="issue"> The inference rules need to be rewritten using the convention that they apply to a syntactic generalization of RDF that allows literals in subject position. This will take some editorial work to complete but should be easier to understand once it is done. The hard work has already been done by terHorst. <br/> <br/> I do not plan to reproduce the completeness proofs which were in the RDF 2004 document. They were unreadable, intimidating, buggy and unnecessary. </p>
</section>
-<section class="appendix" id="MTintro"><h2>Introduction to model theory (Informative)</h2>
+<section class="appendix" id="MTintro"><h2 id="model_theory">Introduction to model theory (Informative)</h2>
///
</section>
-<section class="appendix" id="proofs"><h2>Proofs of Lemmas (Informative)</h2>
+<section class="appendix" id="proofs"><h2 id="proofs">Proofs of Lemmas (Informative)</h2>
///interpolation lemma is now slightly less trivial to prove. Check for possible consequences of this.///
</section>
-<section class="appendix" id="whatnot"><h2>What the semantics does not do (Informative)</h2>
+<section class="appendix" id="whatnot"><h2 id="non_semantics">What the semantics does not do (Informative)</h2>
<p class="issue">Something in here about datasets having no specified semantics, and why. Why using a graph name need not refer to the graph.</p>
-<h3>The RDF vocabulary</h3>
+<h3 id="rdf_vocabulary">The RDF vocabulary</h3>
<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,
or the reification vocabulary intended to enable an RDF graph to describe RDF triples. In this appendix we briefly review the intended meanings of this vocabulary. </p>
@@ -984,7 +984,7 @@
<p><code>_:yyy <ex:property> <ex:foo> .</code></p>
-<h4><a id="Containers">RDF containers</a></h4>
+<h4 a="containers"><a id="Containers">RDF containers</a></h4>
<table border="1">
<tbody>
@@ -1080,7 +1080,7 @@
only finitely many members.</p>
-<h4><a id="collections"></a>RDF collections</h4>
+<a id="collections"></a>RDF collections</h4>
<table border="1">
<tbody>
@@ -1503,7 +1503,7 @@
</section>
<section class='appendix'>
- <h2>Acknowledgements</h2>
+ <h2 id="acknolwedgements">Acknowledgements</h2>
<p>The basic idea of using an explicit extension mapping to allow
self-application without violating the axiom of foundation was
suggested by Christopher Menzel.</p>