--- a/rdf-mt/index.html Sat Oct 12 06:14:08 2013 -0700
+++ b/rdf-mt/index.html Sun Oct 13 10:26:01 2013 -0700
@@ -185,6 +185,9 @@
<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>
+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.
+<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>
@@ -288,7 +291,7 @@
<section>
<h2 id="simple"> Simple Interpretations</h2>
-<p>This section defines the basic notions of interpretation and truth for RDF graphs. All <a>semantic extension</a>s of any vocabulary or higher-level notation encoded in RDF MUST conform to these minimal truth conditions. Other <a>semantic extension</a>s may extend and add to these, but they MUST NOT modify or negate them. For example, because interpretations are mappings which apply to IRIs, a <a>semantic extension</a> cannot interpret different occurrences of a single IRI differently.</p>
+<p>This section defines the basic notions of simple interpretation and truth for RDF graphs. All <a>semantic extension</a>s of any vocabulary or higher-level notation encoded in RDF MUST conform to these minimal truth conditions. Other <a>semantic extension</a>s may extend and add to these, but they MUST NOT modify or negate them. For example, because simple interpretations are mappings which apply to IRIs, a <a>semantic extension</a> cannot interpret different occurrences of a single IRI differently.</p>
<p>The entire semantics applies to <a>RDF graph</a>s, not to <a>RDF source</a>s. An <a>RDF source</a> has a semantic meaning only through the graph that is its value at a given time, or in a given state. Graphs cannot change their semantics with time.</p>
@@ -309,9 +312,9 @@
</tr>
</table>
-<p class="changenote">The 2004 RDF 1.0 semantics defined interpretations relative to a vocabulary.<br/><br/>In the 2004 RDF 1.0 semantics, IL was a total, rather than partial, mapping.<br/><br/> The 2004 RDF 1.0 specification divided literals into 'plain' literals with no type and optional language tags, and typed literals. Usage has shown that it is important that every literal have a type. RDF 1.1 replaces plain literals without language tags by literals typed with the XML Schema <code>string</code> datatype, and introduces the special type <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
+<p class="changenote">The 2004 RDF 1.0 semantics defined simple interpretations relative to a vocabulary.<br/><br/>In the 2004 RDF 1.0 semantics, IL was a total, rather than partial, mapping.<br/><br/> The 2004 RDF 1.0 specification divided literals into 'plain' literals with no type and optional language tags, and typed literals. Usage has shown that it is important that every literal have a type. RDF 1.1 replaces plain literals without language tags by literals typed with the XML Schema <code>string</code> datatype, and introduces the special type <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> for language-tagged strings. The full semantics for typed literals is given in the next section. </p>
-<p class="technote"> Interpretations are required to interpret all <a>name</a>s, and are therefore infinite. This simplifies the exposition. However, RDF can be interpreted using finite structures, supporting decidable algorithms. Details are given in Appendix B. </p>
+<p class="technote"> Simple interpretations are required to interpret all <a>name</a>s, and are therefore infinite. This simplifies the exposition. However, RDF can be interpreted using finite structures, supporting decidable algorithms. Details are given in Appendix B. </p>
<p>IEXT(x), called
@@ -327,7 +330,7 @@
- <p>The denotation of a ground RDF graph in an interpretation I is then given by the following
+ <p>The denotation of a ground RDF graph in a simple interpretation I is then given by the following
rules, where the interpretation is also treated as a function from expressions (names, triples and graphs) to elements of the universe and truth values:</p>
@@ -364,7 +367,7 @@
<p> The final condition implies that the empty graph (the empty set of triples) is always true.</p>
<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>
-<p><a>Semantic extension</a>s may impose further constraints upon interpretation mappings by requiring some IRIs to refer in particular ways. For example, D-interpretations, described below, require some IRIs, understood as <a>identify</a>ing and referring to datatypes, to have a fixed interpretation. </p>
+<p><a>Semantic extension</a>s may impose further constraints upon interpretation mappings by requiring some IRIs to refer in particular ways. For example, D-interpretations, described below, require some IRIs, understood as <a>identify</a>ing and referring to datatypes, to have a fixed denotation. </p>
<section>
<h3 id="blank_nodes">Blank nodes</h3>
@@ -373,7 +376,7 @@
<p>Blank nodes are treated as simply indicating the existence of a thing, without using an IRI to <a>identify</a> any particular thing. This is not the same as assuming that the blank node indicates an 'unknown' IRI.
</p>
-<p> Suppose I is an interpretation and A is a mapping from a set of blank nodes to the universe IR of I. Define the mapping [I+A] to be I on <a>name</a>s, and A on blank nodes on the set: [I+A](x)=I(x) when x is a <a>name</a> and [I+A](x)=A(x) when x is a blank node; and extend this mapping to triples and RDF graphs using the rules given above for ground graphs. Then the semantic conditions for an RDF graph are:</p>
+<p> Suppose I is a simple interpretation and A is a mapping from a set of blank nodes to the universe IR of I. Define the mapping [I+A] to be I on <a>name</a>s, and A on blank nodes on the set: [I+A](x)=I(x) when x is a <a>name</a> and [I+A](x)=A(x) when x is a blank node; and extend this mapping to triples and RDF graphs using the rules given above for ground graphs. Then the semantic conditions for an RDF graph are:</p>
<div class="tabletitle">Semantic condition for blank nodes.</div>
<table border="1">
@@ -388,16 +391,16 @@
</tbody>
</table>
-<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.
+<p>Mappings from blank nodes to referents are not part of the definition of a simple 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
+a denotation by a simple interpretation, reflecting the intuition that
they have no 'global' meaning. </p>
<section class="informative"><h3 id="shared_blank_nodes">Shared blank nodes (Informative)</h3>
<p> The semantics for blank nodes are stated in terms of the truth of a graph. However, when two (or more) graphs share a blank node, their meaning is not fully captured by treating them in isolation. For example, consider the overlapping graphs</p>
<p><img src="RDF11SemanticsDiagrams/example5.jpg" alt="Overlapping Graphs"></p>
-<p> and an interpretation I over the universe {Alice, Bob, Monica, Ruth} with:<br/>
+<p> and a simple interpretation I over the universe {Alice, Bob, Monica, Ruth} with:<br/>
I(<code>ex:Alice</code>)=Alice, I(<code>ex:Bob</code>)=Bob, IEXT(I(<code>ex:hasChild</code>))={<Alice,Monica>,<Bob,Ruth> }<br/></p>
<p>Each of the inner graphs is true under this interpretation, but the two of them together is not, because the three-node graph says that Alice and Bob have a child together. In order to capture the full meaning of graphs sharing a blank node, it is necessary to consider the union graph containing all the triples which contain the blank node.</p>
<p class="technote"> RDF graphs can be viewed as conjunctions of simple atomic sentences in first-order logic, where blank nodes are free variables which are understood to be existential. Taking the union of two graphs is then analogous to syntactic conjunction in this syntax. RDF syntax has no explicit variable-binding quantifiers, so the truth conditions for any RDF graph treat the free variables in that graph as existentially quantified in that graph. Taking the union of graphs which share a blank node changes the implied quantifier scopes.
@@ -416,7 +419,7 @@
<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>satisfiable</dfn> when an 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 <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>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>
@@ -503,7 +506,7 @@
<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 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 identifier by an IRI cannot <a>recognize</a> that IRI, and should treat any literals type with that 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>
@@ -531,7 +534,7 @@
<p>If the literal is <a>ill-typed</a> then the L2V(I(aaa)) mapping has no value, and so the literal cannot denote anything. In this case, any triple containing the literal must be false. Thus, any triple, and hence any graph, containing an <a>ill-typed</a> literal will be <a>D-unsatisfiable</a>, i.e. false in every D-interpretation. This applies only to literals typed with recognized datatype IRIs in D; literals with an unrecognized type IRI are not <a>ill-typed</a> and cannot give rise to a <a>D-unsatisfiable</a> graph. </p>
-<p>The built-in RDF datatype <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> has no <a>ill-typed</a> literals. Any syntactically legal literal with this type will denote a value in every RDF interpretation. The only ill-typed literals of type <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a> are those containing a Unicode code point which does not match the <a href="http://www.w3.org/TR/xml11/#NT-Char"><em>Char</em> production</a> in [[XML10]]. Such strings cannot be written in an XML-compatible surface syntax.
+<p>The special datatype <a href="http://www.w3.org/TR/rdf11-concepts/#dfn-language-tagged-string"><code>rdf:langString</code></a> has no <a>ill-typed</a> literals. Any syntactically legal literal with this type will denote a value in every D-interpretation where D included <code>rdf:langString</code>. The only ill-typed literals of type <a href="http://www.w3.org/TR/xmlschema11-2/#string"><code>xsd:string</code></a> are those containing a Unicode code point which does not match the <a href="http://www.w3.org/TR/xml11/#NT-Char"><em>Char</em> production</a> in [[XML10]]. Such strings cannot be written in an XML-compatible surface syntax.
</p>
@@ -901,7 +904,7 @@
of the RDF axiomatic triples can be derived from the RDFS axiomatic triples
and the semantic conditions on ICEXT,<code> rdfs:domain</code> and <code>rdfs:range</code>. </p>
-<p> Other triples which must be true in all rdfs-interpretations
+<p> Other triples which must be true in all RDFS interpretations
include the following. This is not a complete set.</p>
<div class="tabletitle">Some rdfs-valid triples.</div>
<table border="1">
@@ -1183,7 +1186,8 @@
</section>
<section class="informative appendix"><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>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>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>
@@ -1201,7 +1205,7 @@
<!-- <a href="#emptygraphlemmaprf" class="termref">[Proof]</a> -->
</p>
-<p>The empty graph is true in all interpretations, so is entailed by any graph. If G contains a triple <a b c>, then any interpretation I with IEXT(I(b))={ } makes G false; so the empty graph does not entail G. QED.</p>
+<p>The empty graph is true in all simple interpretations, so is entailed by any graph. If G contains a triple <a b c>, then any simple interpretation I with IEXT(I(b))={ } makes G false; so the empty graph does not entail G. QED.</p>
<p class="fact"> A graph entails all its subgraphs.
<!-- <a href="#subglemprf" class="termref">[Proof]</a> -->
@@ -1221,7 +1225,7 @@
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>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>
@@ -1383,7 +1387,7 @@
If the container is of an ordered type, then the ordering of items in the container is intended to be
indicated by the numerical ordering of the container membership
properties, which are assumed to be single-valued.
- However, these informal interpretations are not reflected in any formal RDF
+ However, these informal conditions are not reflected in any formal RDF
entailments.</p>
@@ -1518,6 +1522,8 @@
<h2 id="ChangeLog">Change Log (informative)</h2>
<p>Changes since Last Call:</p>
<ul>
+<li> Added a general description of the notion of interpretation.
+<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> Brian McBride was acknowledged as series editor of the previous
version. </li>
<li> The wording looking like a definition of RDF Datasets was replaced by