--- a/rdf-mt/index.html Wed Oct 23 19:28:31 2013 +0200
+++ b/rdf-mt/index.html Thu Oct 24 00:02:09 2013 -0500
@@ -161,29 +161,29 @@
<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 be given meanings by other specifications or conventions. 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 entailments follow from those assumptions. </p>
-<p>A particular such set of semantic assumptions is called a <dfn>semantic extension</dfn>. Each <a>semantic extension</a> defines an <dfn>entailment regime</dfn> of entailments which are valid under that extension. RDFS, described later in this document, is one such <a>semantic extension</a>. We will refer to an entailment regime by names such as <em> RDFS entailment</em>, <em>D-entailment</em>, etc. </p>
+<p>A particular such set of semantic assumptions is called a <dfn>semantic extension</dfn>. Each <a>semantic extension</a> defines an <dfn>entailment regime</dfn> (used here in the same sense as in the SPARQL 1.1 Entailment Regime recommendation [[!RDF-SPARQL-ENTAIL]] ) of entailments which are valid under that extension. RDFS, described later in this document, is one such <a>semantic extension</a>. We will refer to entailment regimes by names such as <em> RDFS entailment</em>, <em>D-entailment</em>, etc. </p>
-<p><a>Semantic extension</a>s MAY impose special syntactic conditions or restrictions upon RDF graphs, such as requiring certain triples to be present, or prohibiting particular combinations of IRIs in triples, and MAY consider RDF graphs which do not conform to these conditions to be errors. For example, RDF statements of the form <br/><br/> <code>ex:a rdfs:subClassOf "Thing"^^xsd:string .</code><br/><br/> are prohibited in the OWL <a>semantic extension</a> based on description logics [[!OWL2-SYNTAX]]. In such cases, basic RDF operations such as taking a subset of triples, or combining RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the <a>semantic extension</a>s normatively defined in this document impose such syntactic restrictions on RDF graphs.</p>
+<p><a>Semantic extension</a>s MAY impose special syntactic conditions or restrictions upon RDF graphs, such as requiring certain triples to be present, or prohibiting particular combinations of IRIs in triples, and MAY consider RDF graphs which do not conform to these conditions to be errors. For example, RDF statements of the form <br/><br/> <code>ex:a rdfs:subClassOf "Thing"^^xsd:string .</code><br/><br/> are prohibited in the OWL <a>semantic extension</a> based on description logics [[OWL2-SYNTAX]]. In such cases, basic RDF operations such as taking a subset of triples, or combining RDF graphs, may cause syntax errors in parsers which recognize the extension conditions. None of the <a>semantic extension</a>s normatively defined in this document impose such syntactic restrictions on RDF graphs.</p>
-<p>All entailment regimes MUST be <a>monotonic</a> extensions of the simple entailment regime described in the document, in the sense that if A <a>simply entails</a> B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied. Put another way, a <a>semantic extension</a> cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
+<p>All entailment regimes MUST be <dfn>monotonic</dfn> extensions of the simple entailment regime described in the document, in the sense that if A simply <a>entail</a> B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied. Put another way, a <a>semantic extension</a> cannot "cancel" an entailment made by a weaker entailment regime, although it can treat the result as a syntax error.</p>
</section>
<section>
<h2 id="notation">Notation and Terminology</h2>
- <p>This document uses the following terminology for describing RDF graph syntax, all as defined in the companion RDF Concepts specification [[!RDF11-CONCEPTS]]: <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-iri">IRI</a></em>, <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">RDF triple</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-rdf-graph">RDF graph</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">subject</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">predicate</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples">object</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-rdf-source">RDF source</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-node">node</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-blank-node">blank node</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-literal">literal</a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism">isomorphic</a>, and <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-dataset">RDF datasets</a>.</em> All the definitions in this document apply unchanged to <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a>. </p>
+ <p>This document uses the following terminology for describing RDF graph syntax, all as defined in the companion RDF Concepts specification [[!RDF11-CONCEPTS]]: <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-iri"><dfn>IRI</dfn></a></em>, <em><a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn>RDF triple</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-rdf-graph"><dfn>RDF graph</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn>subject</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn>predicate</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-triples"><dfn>object</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-rdf-source"><dfn>RDF source</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-node"><dfn>node</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-blank-node"><dfn>blank node</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#dfn-literal"><dfn>literal</dfn></a>, <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#graph-isomorphism"><dfn>isomorphic</dfn></a>, and <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-dataset"><dfn>RDF dataset</dfn></a>.</em> All the definitions in this document apply unchanged to <a class="externalDFN" href="http://www.w3.org/TR/rdf11-concepts/#section-generalized-rdf">generalized RDF triples, graphs, and datasets</a>. </p>
<p>
-An <em>interpretation</em> is a mapping from IRIs and literals into a set, together with some constraints upon the set and the mapping. This document defines various notions of interpretation, each corresponding in a standard way to an entailment regime. These are identified by prefixes such as <em>simple interpretation</em>, etc., and are defined in later sections. The unqualified term <em>interpretation</em> is usually used to any compatible kind of interpretation in general, but if clear from the context might refer to a specific kind of interpretation.
+An <dfn>interpretation</dfn> is a mapping from IRIs and literals into a set, together with some constraints upon the set and the mapping. This document defines various notions of interpretation, each corresponding in a standard way to an entailment regime. These are identified by prefixes such as <em>simple interpretation</em>, etc., and are defined in later sections. The unqualified term <em>interpretation</em> is usually used to refer to any compatible kind of interpretation in general, but if clear from the context might refer to a specific kind of interpretation.
<p>
-<p>The words <dfn>denotes</dfn> and <dfn>refers to</dfn> are used interchangeably as synonyms for the relationship between an IRI or literal and what it refers to in a given interpretation, itself called the <dfn>referent</dfn> or <dfn>denotation</dfn>. IRI meanings may also be determined by other constraints external to the RDF semantics; when we wish to refer to such an externally defined naming relationship, we will use the word <dfn>identify</dfn> and its cognates. For example, the fact that the IRI <code>http://www.w3.org/2001/XMLSchema#decimal</code> is widely used as the name of a datatype described in the XML Schema document [[XMLSCHEMA11-2]] might be described by saying that the IRI <em>identifies</em> that datatype. If an IRI identifies something it may or may not refer to it in a given interpretation, depending on how the semantics is specified. For example, an IRI used as a graph name <a>identify</a>ing a named graph in an <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="external">RDF dataset</a> may refer to something different from the graph it identifies. </p>
+<p>The words <dfn>denote</dfn><strong>s</strong> and <dfn>refers to</dfn> are used interchangeably as synonyms for the relationship between an IRI or literal and what it refers to in a given interpretation, itself called the <dfn>denotation</dfn> or <dfn>referent</dfn>. IRI meanings may also be determined by other constraints external to the RDF semantics; when we wish to refer to such an externally defined naming relationship, we will use the word <dfn>identify</dfn> and its cognates. For example, the fact that the IRI <code>http://www.w3.org/2001/XMLSchema#decimal</code> is widely used as the name of a datatype described in the XML Schema document [[XMLSCHEMA11-2]] might be described by saying that the IRI <em>identifies</em> that datatype. If an IRI identifies something it may or may not refer to it in a given interpretation, depending on how the semantics is specified. For example, an IRI used as a graph name <a>identify</a>ing a named graph in an <a href="http://www.w3.org/TR/rdf11-concepts/#section-dataset" class="external">RDF dataset</a> may refer to something different from the graph it identifies. </p>
<p>Throughout this document, the equality sign = indicates strict identity. The statement "A = B" means that there is one entity to which both expressions "A" and "B" refer. Angle brackets < x, y > are used to indicate an ordered pair
of x and y.</p>
-<p>Throughout this document, RDF graphs and other fragments of RDF abstract syntax are written using the notational conventions of the Turtle syntax [[!TURTLE]]. The namespace prefixes <code>rdf:</code> <code>rdfs:</code> and <code>xsd:</code> are used as in [[!RDF11-CONCEPTS]], <a href="http://www.w3.org/TR/rdf11-concepts/#vocabularies">section 1.4</a>. When the exact IRI does not matter, the prefix <code>ex:</code> is used. When stating general rules or conditions we use three-character variables such as aaa, xxx, sss to indicate arbitrary IRIs, literals, or other components of RDF syntax. Some cases are illustrated by node-arc diagrams showing the graph structure directly.</p>
+<p>Throughout this document, <a>RDF graph</a>s and other fragments of RDF abstract syntax are written using the notational conventions of the Turtle syntax [[!TURTLE]]. The namespace prefixes <code>rdf:</code> <code>rdfs:</code> and <code>xsd:</code> are used as in [[!RDF11-CONCEPTS]], <a href="http://www.w3.org/TR/rdf11-concepts/#vocabularies">section 1.4</a>. When the exact IRI does not matter, the prefix <code>ex:</code> is used. When stating general rules or conditions we use three-character variables such as aaa, xxx, sss to indicate arbitrary IRIs, literals, or other components of RDF syntax. Some cases are illustrated by node-arc diagrams showing the graph structure directly.</p>
<p>A <dfn>name</dfn> is any IRI or literal. A typed literal contains
two <a>name</a>s: itself and its internal type
@@ -411,15 +411,15 @@
<section id="simpleentailment"><h2>Simple Entailment</h2>
-<p>Following standard terminology, we say that I <dfn>satisfies</dfn> E when I(E)=true, that E is <dfn>simply satisfiable</dfn> when a simple interpretation exists which satisfies it, (otherwise <dfn>unsatisfiable</dfn>), and that a graph G <dfn>simply entails</dfn> a graph E when every interpretation which satisfies G also satisfies E. </p>
+<p>Following standard terminology, we say that I (simply) <dfn>satisfies</dfn> E when I(E)=true, that E is (simply) <dfn>satisfiable</dfn> when a simple interpretation exists which satisfies it, otherwise (simply) <dfn>unsatisfiable</dfn>, and that a graph G simply <dfn>entail</dfn><strong>s</strong> a graph E when every interpretation which satisfies G also satisfies E. If two graphs E and F each entail the other then they are logically <dfn>equivalent</dfn>.</p>
<p>In later sections these notions will be adapted to other classes of interpretations, but throughout this section 'entailment' should be interpreted as meaning simple entailment.
</p>
<p class="technote">We do not define a notion of entailment between sets of graphs. To determine whether a set of graphs entails a graph, the graphs in the set must first be combined into one graph, either by taking the union or the merge of the graphs. Unions preserve the common meaning of shared blank nodes, while merging effectively ignores any sharing of blank nodes. Merging the set of graphs produces the same definition of entailment by a set that was defined in the 2004 RDF 1.0 specification.</p>
- <p><a id="defvalid">Any process which constructs a graph E from
+ <p>Any process which constructs a graph E from
some other graph S is (simply) <dfn>valid</dfn> if S
- simply entails E in every case, otherwise <dfn>invalid.</dfn></a></p>
+ simply entails E in every case, otherwise <dfn>invalid.</dfn></p>
<p>The fact that an inference is valid should not be understood as meaning that any RDF application is obliged or required to make the inference. Similarly, the logical invalidity of some RDF transformation or process does not mean that the process is incorrect or prohibited. Nothing in this specification requires or prohibits any particular operations on RDF graphs or sources. Entailment and validity are concerned solely with establishing the conditions on such operations which guarantee the preservation of truth. While logically invalid processes, which do not follow valid entailments, are not prohibited, users should be aware that they may be at risk of introducing falsehoods into true RDF data. Nevertheless, particular uses of logically invalid processes may be justified and appropriate for data processing under circumstances where truth can be ensured by other means. </p>
@@ -432,9 +432,9 @@
<h3 id="simple_entailment_properties">Properties of simple entailment (Informative) </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 Appendix C. </p>
-<p class="fact">Every graph is satisfiable.</p>
+<p class="fact">Every graph is simply satisfiable.</p>
-<p>This does not hold for extended notions of interpretation. For example, a graph containing an <a>ill-typed</a> literal is <a>D-unsatisfiable</a>.</p>
+<p>This does not always hold for extended notions of interpretation. For example, a graph containing an <a>ill-typed</a> literal is <a>D-unsatisfiable</a>.</p>
<p>The following <dfn>interpolation</dfn> <strong>lemma</strong> </p>
@@ -446,27 +446,27 @@
terms. To detect whether one RDF graph simply entails another, check that
there is some instance of the entailed graph which is a subset of the first graph. </p>
-<p class="technote">This is clearly decidable, but it is also difficult to determine in general, since one can encode the NP-hard subgraph problem (detecting whether one mathematical graph is a subgraph of another) as detecting simple entailment between RDF graphs. This construction (due to Jeremy Carroll) uses graphs containing many blank nodes, which are unlikely to occur in practice. The complexity of checking simple entailment is reduced by having fewer blank nodes in the conclusion E. When E is a <a>ground</a> graph, it is simply a matter of checking the subset relationship on sets of triples.</p>
+<p class="technote">This is clearly decidable, but it is also difficult to determine in general, since one can encode the NP-hard subgraph problem (detecting whether one mathematical graph is a subgraph of another) as detecting simple entailment between RDF graphs. This construction (due to Jeremy Carroll) uses graphs all of whose nodes are blank nodes. The complexity of checking simple entailment is reduced by having fewer blank nodes in the conclusion E. When E is a <a>ground</a> graph, it is simply a matter of checking the subset relationship on sets of triples.</p>
<p><a>Interpolation</a> has a number of direct consequences, for example:</p>
-<p class="fact"> The <a>empty graph</a> is entailed by
- any graph, and does not entail any graph except itself.
+<p class="fact"> The <a>empty graph</a> is simply entailed by
+ any graph, and does not simply entail any graph except itself.
<!-- <a href="#emptygraphlemmaprf" class="termref">[Proof]</a> -->
</p>
-<p class="fact"> A graph entails all its subgraphs.
+<p class="fact"> A graph simply entails all its subgraphs.
<!-- <a href="#subglemprf" class="termref">[Proof]</a> -->
</p>
<p class="fact"> A graph
- is entailed by any of its <a>instance</a>s.
+ is simply entailed by any of its <a>instance</a>s.
<!-- <a href="#instlemprf" class="termref"> [Proof]</a> -->
</p>
<p class="fact"> If
E is a <a>lean</a> graph and E' is a <a>proper instance</a> of E, then E does
- not entail E'.
+ not simply entail E'.
</p>
-<p class="fact"> If S is a subgraph of S' and S entails E, then S' entails E.
+<p class="fact"> If S is a subgraph of S' and S simply entails E, then S' simply entails E.
<!-- <a href="#monotonicitylemmaprf" class="termref"> [Proof]</a> -->
</p>
<p class="fact">
@@ -475,19 +475,19 @@
</p>
<p>The property just above is called <em>compactness</em> - RDF is compact. As RDF graphs can be infinite, this is sometimes important.</p>
-<p class="fact"> If E contains an IRI which does not occur anywhere in S, then S does not entail E.</p>
+<p class="fact"> If E contains an IRI which does not occur anywhere in S, then S does not simply entail E.</p>
</section>
</section>
<section class="informative"><h2 id="skolemization">Skolemization (Informative)</h2>
-<p><a class="externaldefinition">Skolemization</a> 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 <a href="http://www.w3.org/TR/rdf11-concepts/#section-skolemization">Section 3.5</a> of [[!RDF11-CONCEPTS]] for a fuller discussion. </p>
+<p><a class="externaldefinition"><dfn>Skolemization</dfn></a> 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 <a href="http://www.w3.org/TR/rdf11-concepts/#section-skolemization">Section 3.5</a> of [[!RDF11-CONCEPTS]] for a fuller discussion. </p>
<p> Suppose G is a graph containing blank nodes and sk is a skolemization mapping from the blank nodes in G to the skolem IRIs which are substituted for them, so that sk(G) is a skolemization of G. Then the semantic relationship between them can be summarized as follows. </p>
<p class="fact"> sk(G) simply entails G (since sk(G) is an instance of G.)</p>
-<p class="fact"> G does not entail sk(G) (since sk(G) contains IRIs not in G.) </p>
-<p class="fact"> For any graph H, if sk(G) entails H then there is a graph H' such that G entails H' and H=sk(H') . </p>
+<p class="fact"> G does not simply entail sk(G) (since sk(G) contains IRIs not in G.) </p>
+<p class="fact"> For any graph H, if sk(G) simply entails H then there is a graph H' such that G entails H' and H=sk(H') . </p>
<p class="fact"> For any graph H which does not contain any of the "new" IRIs introduced into sk(G), sk(G) simply entails H if and only if G simply entails H.
</p>
@@ -498,14 +498,14 @@
<section><h2 id="datatypes">Literals and datatypes</h2>
<p class="changenote"> In the 2004 RDF 1.0 specification, datatype D-entailment was defined as a <a>semantic extension</a> 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>
-<p> Datatypes are <a title="identify">identified</a> by IRIs. Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on simple interpretations. where D is the set of <dfn>recognize</dfn><strong>d</strong> datatype IRIs. We assume that a recognized IRI <a title="identify">identifies</a> a unique datatype wherever it occurs, and the semantics requires that it refers to this identified datatype. The exact mechanism by which an IRI <a title="identify">identifies</a> a datatype IRI is considered to be external to the semantics. RDF processors which are not able to determine which datatype is identifier by an IRI cannot <a>recognize</a> that IRI, and should treat any literals type with that IRI as unknown names. </p>
+<p> Datatypes are <a title="identify">identified</a> by IRIs. Interpretations will vary according to which IRIs they recognize as denoting datatypes. We describe this using a parameter D on simple interpretations. where D is the set of <dfn>recognize</dfn><strong>d</strong> datatype IRIs. We assume that a recognized IRI <a title="identify">identifies</a> a unique datatype wherever it occurs, and the semantics requires that it refers to this identified datatype. The exact mechanism by which an IRI <a title="identify">identifies</a> a datatype IRI is considered to be external to the semantics. RDF processors which are not able to determine which datatype is identified by an IRI cannot <a>recognize</a> that IRI, and should treat any literals with that IRI as their datatype IRI as unknown names. </p>
-<p class="changenote">In the 2004 RDF 1.0 specification, the semantics of datatypes referred to datatype maps. The current treatment subsumes datatype maps into the interpretation mapping on recognized IRIs.</p>
+<p class="changenote">In the 2004 RDF 1.0 specification, the semantics of datatypes referred to datatype maps. The current treatment subsumes datatype maps into the interpretation mapping on recognized IRIs.The <dfn>datatype map</dfn> corresponding to D is exactly the restriction of a D-interpretation mapping to the set D of recognized datatypes. The 2004 definitions permitted "non-standard" datatype maps which map IRIs to datatypes they do not <a>identify</a> (such as one that maps the IRI '<code>http://www.w3.org/2001/XMLSchema#decimal</code>' to the datatype identified by <code>http://www.w3.org/2001/XMLSchema#gYearMonth</code> ). Semantic extensions based on such non-standard mappings are not sanctioned by this specification.</p>
<p>RDF literals and datatypes are fully described in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes"> Section 5</a> of [[!RDF11-CONCEPTS]]. In summary: RDF literals are either language-tagged strings, or datatyped literals which
-combine a string and an IRI <a>identify</a>ing a datatype. A datatype is understood to define a partial mapping, called the <dfn>lexical-to-value mapping</dfn>, from character strings to values. The function <dfn>L2V</dfn> maps datatypes to their lexical-to-value mapping. A literal with datatype d denotes the value obtained by applying this mapping to the character string sss: L2V(d)(sss). If the lexical-to-value mapping gives no value for the literal string, then the literal has no referent. The <dfn>value space</dfn> of a datatype is the range of the <a>lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space of the type, or fails to refer at all. An <dfn>ill-typed</dfn> literal is one whose datatype IRI is <a>recognize</a>d, but whose character string is assigned no value by the <a>lexical-to-value mapping</a> for that datatype. </p>
+combine a string and an IRI <a>identify</a>ing a datatype. A datatype is understood to define a partial mapping, called the <dfn>lexical-to-value mapping</dfn>, from a lexical space (a set of character strings) to values. The function <dfn>L2V</dfn> maps datatypes to their lexical-to-value mapping. A literal with datatype d denotes the value obtained by applying this mapping to the character string sss: L2V(d)(sss). If the literal string is not in the lexical space, so that the lexical-to-value mapping gives no value for the literal string, then the literal has no referent. The <dfn>value space</dfn> of a datatype is the range of the <a>lexical-to-value mapping</a>. Every literal with that type either refers to a value in the value space of the type, or fails to refer at all. An <dfn>ill-typed</dfn> literal is one whose datatype IRI is <a>recognize</a>d, but whose character string is assigned no value by the <a>lexical-to-value mapping</a> for that datatype. </p>
-<p> RDF processors are not REQUIRED to <a>recognize</a> any datatype IRIs other than <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> and <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a>, but when IRIs listed in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes">Section 5</a> of [[!RDF11-CONCEPTS]] are <a>recognize</a>d, they MUST be interpreted as described there, and when the IRI <code>rdf:PlainLiteral</code> is <a>recognize</a>d, it MUST be interpreted to refer to the datatype defined in [[!RDF-PLAIN-LITERAL]]. RDF processors MAY recognize other datatype IRIs, but when other datatype IRIs are <a>recognize</a>d, the mapping between a <a>recognize</a>d IRI and the datatype it refers to MUST be specified unambiguously, and MUST be fixed during all RDF transformations or manipulations.</p>
+<p> RDF processors are not required to <a>recognize</a> any datatype IRIs other than <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> and <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a>, but when IRIs listed in <a href="http://www.w3.org/TR/rdf11-concepts/#section-Datatypes">Section 5</a> of [[!RDF11-CONCEPTS]] are <a>recognize</a>d, they MUST be interpreted as described there, and when the IRI <code>rdf:PlainLiteral</code> is <a>recognize</a>d, it MUST be interpreted to refer to the datatype defined in [[!RDF-PLAIN-LITERAL]]. RDF processors MAY recognize other datatype IRIs, but when other datatype IRIs are <a>recognize</a>d, the mapping between a <a>recognize</a>d IRI and the datatype it refers to MUST be specified unambiguously, and MUST be fixed during all RDF transformations or manipulations.</p>
<p>Literals with <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> as their datatype are an exceptional case which are given a special treatment. The IRI <code>rdf:langString</code> is classified as a datatype IRI, and interpreted to refer to a datatype, even though no L2V mapping is defined for it. The value space of <code>rdf:langString</code> is the set of all pairs of a string with a language tag. The semantics of literals with this as their type are given below. </p>
@@ -513,7 +513,7 @@
<section id="D_interpretations"><h2>D-interpretations</h2>
-<p>Let D be a set of IRIs <a>identify</a>ing datatypes. A <dfn>(simple) D-interpretation</dfn> is a <a>simple interpretation</a> which satisfies the following conditions:</p>
+<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>
<table border="1">
@@ -582,6 +582,26 @@
<p >RDF interpretations impose extra semantic conditions on <code>xsd:string</code> and part of the infinite
set of IRIs with the namespace prefix <code>rdf:</code> .
+<div >
+ <table border="1">
+ <tbody>
+ <tr>
+ <td ><dfn>RDF vocabulary</dfn></td>
+ </tr>
+
+ <tr>
+ <td ><code>rdf:type rdf:subject rdf:predicate rdf:object
+ rdf:first rdf:rest rdf:value rdf:nil
+ rdf:List rdf:langString rdf:Property rdf:_1 rdf:_2
+ ...
+ </div>
+</code></td>
+ </tr>
+ </tbody>
+ </table>
+ </div>
+
+
<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>
<table border="1">
@@ -629,9 +649,9 @@
<h3 id="rdf_entail">RDF entailment</h3>
-<p>S <dfn>RDF entail</dfn><strong>s</strong> E <strong>recognizing D</strong> when every <a>RDF interpretation recognizing D</a> which satisfies S also satisfies E. When D is {<code>rdf:langString</code>, <code>xsd:string</code>} then we simply say S <strong>RDF entails</strong> E. </p>
+<p>S <dfn>RDF entail</dfn><strong>s</strong> E <strong>recognizing D</strong> when every <a>RDF interpretation</a> recognizing D which satisfies S also satisfies E. When D is {<code>rdf:langString</code>, <code>xsd:string</code>} then we simply say S <strong>RDF entails</strong> E. E is <dfn>RDF unsatisfiable</dfn><strong> (recognizing D)</strong> when it has no satisfying <a>RDF interpretation</a> (recognizing D).</p>
-<p>The properties of <a>simple entailment</a> described earlier do not all apply to <a>RDF entail</a>ment. For example, all the RDF axioms are true in every <a>RDF interpretation</a>, and so are <a>RDF entail</a>ed by the empty graph, contradicting <a>interpolation</a> for RDF entailment. </p>
+<p>The properties of simple entailment described earlier do not all apply to <a>RDF entail</a>ment. For example, all the RDF axioms are true in every <a>RDF interpretation</a>, and so are <a>RDF entail</a>ed by the empty graph, contradicting <a>interpolation</a> for RDF entailment. </p>
<section class="informative"><h4 id="rdf_entailment_patterns">Patterns of RDF entailment (Informative)</h4>
@@ -1085,7 +1105,7 @@
3. Apply the RDF (or RDF and RDFS) inference patterns as rules, adding each conclusion to the graph, to exhaustion; that is, until they generate no new triples. <br/>
4. Determine if E has an instance which is a subset of the set, i.e. whether the enlarged set simply entails E.</p>
-<p>This process is clearly <a>correct</a>, in that if it gives a positive result then indeed S does RDF (RDFS) entail E. It is not, however, <a>complete</a>: there are cases of S entailing E which are not detectable by this process. Examples include:</p>
+<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>
<table border="1" >
<tbody>
@@ -1217,7 +1237,7 @@
G simply entails a graph E if and only if a subgraph of G is an instance of E.
</p>
-<p>If a subgraph E' of G is an instance of E then G entails E' which entails E, so G entails E. Now suppose G entails E, and consider the <a>Herbrand interpretation</a> I of G defined as follows. IR contains the <a>name</a>s and blank nodes which occur in the graph, with I(n)=n for each <a>name</a> n; n is in IP and <a, b> in IEXT(n) just when the triple <a n b> is in the graph. (For IRIs which do not occur in the graph, assign them values in IR at random.) I satisfies every triple <s p o> in E; that is, for some mapping A from the blank nodes of E to the vocabulary of G, the triple <[I+A](s) I(p) [I+A](o)> occurs in G. But this is an instance of <s p o> under the instance mapping A; so an instance of E is a subgraph of G. QED.</p>
+<p>If a subgraph E' of G is an instance of E then G entails E' which entails E, so G entails E. Now suppose G entails E, and consider the <a href="http://en.wikipedia.org/wiki/Herbrand_interpretation">Herbrand interpretation</a> I of G defined as follows. IR contains the <a>name</a>s and blank nodes which occur in the graph, with I(n)=n for each <a>name</a> n; n is in IP and <a, b> in IEXT(n) just when the triple <a n b> is in the graph. (For IRIs which do not occur in the graph, assign them values in IR at random.) I satisfies every triple <s p o> in E; that is, for some mapping A from the blank nodes of E to the vocabulary of G, the triple <[I+A](s) I(p) [I+A](o)> occurs in G. But this is an instance of <s p o> under the instance mapping A; so an instance of E is a subgraph of G. QED.</p>
<p class="fact">if E is lean and E' is a proper instance of E, then E does not entail E'.</p>
<p>Suppose E entails E', then a subgraph of E is an instance of E', which is a proper instance of E; so a subgraph of E is a proper instance of E, so E is not lean. QED.</p>
@@ -1333,11 +1353,11 @@
<table border="1">
<tbody>
<tr>
- <td class="othertable"><strong>RDF Container Vocabulary</strong></td>
+ <td class="othertable"><strong>RDF(S) Container Vocabulary</strong></td>
</tr>
<tr>
<td class="othertable"><code>rdf:Seq rdf:Bag rdf:Alt rdf:_1 rdf:_2
- ...</code></td>
+ ... rdfs:member rdfs:Container rdfs:ContainerMembershipProperty</code></td>
</tr>
</tbody>
</table>
@@ -1396,7 +1416,7 @@
_:xxx rdf:_2 ex:a .</code></p>
<p>(If this conclusion were <a>valid</a>, then the result of
- adding it to the original graph would be <a>entailed</a> by the graph, and this would assert that both elements were in both
+ adding it to the original graph would be <a>entail</a>ed by the graph, and this would assert that both elements were in both
positions. This is a consequence of the fact that RDF is a purely
assertional language.)</p>
@@ -1514,6 +1534,10 @@
<h2 id="ChangeLog">Change Log (informative)</h2>
<p>Changes since Last Call:</p>
<ul>
+<li> Repaired several broken internal links and typos.</li>
+<li> Added table of RDF vocabulary. </li>
+<li> Added text mentioning lexical spaces in datatypes.</li>
+<li> Added extended change note defining datatype map.</li>
<li> Removed informative section on intuitive summary of truth conditions </li>
<li> Added a general description of the notion of interpretation. </li>
<li> Adjusted several uses of "interpretation" and related terminology to state the particular kind of interpretation in question or use a more appropriate term. </li>