authorGuus Schreiber <>
Mon, 01 Apr 2013 16:14:29 +0200
changeset 714 e682175153b3
parent 713 6ffbd18754da
child 715 ad4c341cfa0c
--- a/rdf-mt/index.html	Mon Apr 01 16:07:46 2013 +0200
+++ b/rdf-mt/index.html	Mon Apr 01 16:14:29 2013 +0200
@@ -265,7 +265,7 @@
   <div class="tabletitle">Semantic conditions for ground graphs.</div>
-  <table border="2">
+  <table border="1">
@@ -307,7 +307,7 @@
 <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 names, and A on blank nodes on the set: [I+A](x)=I(x) when x is a name 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. </p>
     <div  class="tabletitle">Semantic condition for blank nodes.</div>
-      <table border="2">
+      <table border="1">
@@ -355,10 +355,10 @@
 <p><strong>Empty Graph Lemma.</strong> The empty set of triples is entailed by 
   any graph, and does not entail any graph except itself. <a href="#emptygraphlemmaprf" class="termref">[Proof]</a></p>
-<p><a name="subglem" id="subglem"><strong>Subgraph Lemma.</strong></a> A graph 
+<p><a id="subglem"><strong>Subgraph Lemma.</strong></a> A graph 
   entails all its <a
     href="#defsubg" class="termref">subgraphs</a>. <a href="#subglemprf" class="termref">[Proof]</a></p>
-<p><a name="instlem" id="instlem"><strong>Instance Lemma.</strong></a> A graph 
+<p><a id="instlem"><strong>Instance Lemma.</strong></a> A graph 
   is entailed by any of its <a
     href="#definst" class="termref">instances</a>.<a href="#instlemprf" class="termref"> [Proof]</a></p>
@@ -373,7 +373,7 @@
 <p>Say that a set S of graphs is <dfn>segregated</dfn> when no two graphs in the set share a blank node.</p>
-<p><a name="mergelem" id="mergelem"><strong>Merging lemma.</strong></a> The union 
+<p><a id="mergelem"><strong>Merging lemma.</strong></a> The union 
   of a segregated set S of RDF graphs is entailed by S, and entails every member of S. <a href="#mergelemprf" class="termref">[Proof]</a></p>
@@ -384,7 +384,7 @@
     href="#glossModeltheory" class="termref">model theory</a> is
     concerned.  In general, we will not usually bother to distinguish between a set of graphs and the single graph formed by taking their union. </p>
         <p>The main result for simple entailment is:</p>
-<p><a name="interplemma" id="interplemma"><strong>Interpolation Lemma.</strong> 
+<p><a id="interplemma"><strong>Interpolation Lemma.</strong> 
   S entails a graph E if and only if a subgraph of S is an instance of E. </a><a href="#interplemmaprf" class="termref">[Proof]</a></p>
 <p>The interpolation lemma completely characterizes simple entailment in syntactic 
   terms. To tell whether a set of RDF graphs simply entails another, check that 
@@ -392,14 +392,14 @@
   of the original set of graphs. </p>
 <p>This is clearly decidable, but it is also theoretically very hard 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. (///Refer to Jeremy Carroll.///) </p>
-<p><a name="Anonlem1" id="Anonlem1"><strong>Anonymity lemma.</strong></a> Suppose 
+<p><a id="Anonlem1"><strong>Anonymity lemma.</strong></a> Suppose 
   E is a <a>lean</a> graph and E' is a proper instance of E. Then E does 
   not entail E'. <a href="#Anonlem1prf" class="termref">[Proof]</a></p>
-<p><strong><a name="monotonicitylemma" id="monotonicitylemma"></a>Monotonicity 
+<p><strong><a id="monotonicitylemma"></a>Monotonicity 
   Lemma</strong>. Suppose S is a subgraph of S' and S entails E. Then S' entails 
   E.<a href="#monotonicitylemmaprf" class="termref"> [Proof]</a></p>
-<p><strong><a name="compactlemma" id="compactlemma"></a>Compactness Lemma</strong>. 
+<p><strong><a id="compactlemma"></a>Compactness Lemma</strong>. 
   If S entails E and E is a finite graph, then some finite subset S' of S entails 
   E. <a href="#compactlemmaprf" class="termref"> [Proof]</a></p>
@@ -445,7 +445,7 @@
 <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>
-<table border="1" class="semantictable" summary="datatype semantic condition">
+<table border="1" class="semantictable">
 <tr><td>If <code>rdf:langString</code> is in D, then for every language-tagged string E with lexical form sss and language tag ttt, IL(E)= &lt; sss, ttt &gt; </td></tr>
 <tr><td>For every other IRI aaa in D, and every literal "sss"^^aaa, IL("sss"^^aaa) = L2V(I(aaa))(sss)</td></tr>
@@ -487,13 +487,13 @@
 <p>An <dfn>rdf-D-interpretation</dfn>  I is a D-interpretation 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" summary="RDF semantic condition">
+<table  border="1">
-      <td class="semantictable"><a name="rdfsemcond1" id="rdfsemcond1"></a>x is 
+      <td class="semantictable"><a id="rdfsemcond1"></a>x is 
         in IP if and only if &lt;x, I(<code>rdf:Property</code>)&gt; is in IEXT(I(<code>rdf:type</code>))</td>
-<tr><td class="semantictable"><a name="rdfsemcond3" id="rdfsemcond3">For every IRI aaa in D, &lt; x, I(aaa) &gt; is in IEXT(I(<code>rdf:type</code>)) if and only if x is in the value space of I(aaa)</td></tr>
+<tr><td class="semantictable"><a id="rdfsemcond3">For every IRI aaa in D, &lt; x, I(aaa) &gt; is in IEXT(I(<code>rdf:type</code>)) if and only if x is in the value space of I(aaa)</td></tr>
@@ -501,9 +501,9 @@
     <p>and satisfies every triple in the following infinite set:</p> 
  <div class="tabletitle">RDF axioms.</div> 
-  <table  border="1" summary="RDF axiomatic triples">
+  <table  border="1">
-      <td class="ruletable"><a name="RDF_axiomatic_triples" id="RDF_axiomatic_triples"> </a><code>rdf:type rdf:type rdf:Property .<br/>
+      <td class="ruletable"><a id="RDF_axiomatic_triples"> </a><code>rdf:type rdf:type rdf:Property .<br/>
         rdf:subject rdf:type rdf:Property .<br/>
         rdf:predicate rdf:type rdf:Property .<br/>
         rdf:object rdf:type rdf:Property .<br/>
@@ -525,7 +525,7 @@
 <p>An <em>rdf-interpretation</em>, or <em>RDF interpretation</em>, is an rdf-{<code>rdf:langString</code>, <code>xsd:string</code> }-interpretation, i.e. an rdf-D-Interpretation with a minimal set D. The datatypes <code>rdf:langString</code> and <code>xsd:string</code> MUST be recognized by all RDF interpretations. </p><p>The RDF built-in datatypes <code>rdf:XMLLiteral</code> and <code>rdf:HTML</code> are defined in ///RDF Concepts///. RDF interpretations are not required to recognize these datatypes. </p>
-<h3><a name="rdf_entail" id="rdf_entail"></a>RDF entailment</h3>
+<h3><a id="rdf_entail"></a>RDF entailment</h3>
 <p>S <i>rdf-D-entails</i> E when every rdf-D-interpretation which satisfies every 
   member of S also satisfies E. </p>
@@ -551,7 +551,7 @@
   with more complex semantic constraints:</p>
     <div class="c1">
-      <table border="1" summary="RDFS vocabulary">
+      <table border="1">
             <td class="othertable"><strong>RDFS vocabulary</strong></td>
@@ -593,7 +593,7 @@
   <table  border="1">
-    <td class="semantictable"> <p><a name="rdfssemcond1" id="rdfssemcond1"></a>ICEXT(y) is defined to be { x : &lt; x,y &gt; is in IEXT(I(<code>rdf:type</code>)) }</p>
+    <td class="semantictable"> <p><a id="rdfssemcond1"></a>ICEXT(y) is defined to be { x : &lt; x,y &gt; is in IEXT(I(<code>rdf:type</code>)) }</p>
         <p>IC is defined to be ICEXT(I(<code>rdfs:Class</code>))</p>
         <p>LV is defined to be ICEXT(I(<code>rdfs:Literal</code>))</p>
         <p>ICEXT(I(<code>rdfs:Resource</code>)) = IR</p>
@@ -604,39 +604,39 @@
-    <td class="semantictable"> <p><a name="rdfssemcond2" id="rdfssemcond2"></a>If 
+    <td class="semantictable"> <p><a id="rdfssemcond2"></a>If 
         &lt; x,y &gt; is in IEXT(I(<code>rdfs:domain</code>)) and &lt; u,v &gt; is 
         in IEXT(x) then u is in ICEXT(y)</p></td>
-    <td class="semantictable"> <p><a name="rdfssemcond3" id="rdfssemcond3"></a>If 
+    <td class="semantictable"> <p><a id="rdfssemcond3"></a>If 
         &lt; x,y &gt; is in IEXT(I(<code>rdfs:range</code>)) and &lt; u,v &gt; is 
         in IEXT(x) then v is in ICEXT(y)</p></td>
-    <td class="semantictable"><p><a name="rdfssemcond4" id="rdfssemcond4"></a>IEXT(I(<code>rdfs:subPropertyOf</code>)) 
+    <td class="semantictable"><p><a id="rdfssemcond4"></a>IEXT(I(<code>rdfs:subPropertyOf</code>)) 
       is transitive and reflexive on IP</p></td>
-    <td class="semantictable"> <p><a name="rdfssemcond5" id="rdfssemcond5"></a>If 
+    <td class="semantictable"> <p><a id="rdfssemcond5"></a>If 
         &lt;x,y&gt; is in IEXT(I(<code>rdfs:subPropertyOf</code>)) then x and 
         y are in IP and IEXT(x) is a subset of IEXT(y)</p></td>
-    <td class="semantictable"><p><a name="rdfssemcond6" id="rdfssemcond6"></a>If 
+    <td class="semantictable"><p><a id="rdfssemcond6"></a>If 
         x is in IC then &lt; x, I(<code>rdfs:Resource</code>) &gt; is in IEXT(I(<code>rdfs:subClassOf</code>))</p></td>
-       <td class="semantictable"><p><a name="rdfssemcond8" id="rdfssemcond8"></a>IEXT(I(<code>rdfs:subClassOf</code>)) 
+       <td class="semantictable"><p><a id="rdfssemcond8"></a>IEXT(I(<code>rdfs:subClassOf</code>)) 
       is transitive and reflexive on IC</p></td>
-    <td class="semantictable"> <p><a name="rdfssemcond7" id="rdfssemcond7"></a>If 
+    <td class="semantictable"> <p><a id="rdfssemcond7"></a>If 
         &lt; x,y &gt; is in IEXT(I(<code>rdfs:subClassOf</code>)) then x and y are 
         in IC and ICEXT(x) is a subset of ICEXT(y)</p></td>
@@ -644,14 +644,14 @@
-      <td class="semantictable"><p><a name="rdfssemcond9" id="rdfssemcond9"></a>If 
+      <td class="semantictable"><p><a id="rdfssemcond9"></a>If 
         x is in ICEXT(I(<code>rdfs:ContainerMembershipProperty</code>)) then:<br/>
         &lt; x, I(<code>rdfs:member</code>) &gt; is in IEXT(I(<code>rdfs:subPropertyOf</code>))<br/>
-    <td class="semantictable"><p><a name="rdfssemcond10" id="rdfssemcond10"></a>If 
+    <td class="semantictable"><p><a id="rdfssemcond10"></a>If 
         x is in ICEXT(I(<code>rdfs:Datatype</code>)) then <span >&lt; x, 
         I(<code>rdfs:Literal</code>) &gt; is in IEXT(I(<code>rdfs:subClassOf</code>))</span></p></td>
@@ -664,7 +664,7 @@
     <p><a id="RDFS_axiomatic_triples" name="RDFS_axiomatic_triples">  </a>
 	  <div class="tabletitle">RDFS axiomatic triples.</div>
-  <table  border="1" summary="RDFS axioms">
+  <table  border="1">
@@ -673,7 +673,7 @@
       rdfs:domain rdfs:domain rdf:Property .<br/>
       rdfs:range rdfs:domain rdf:Property .<br/>
       rdfs:subPropertyOf rdfs:domain rdf:Property .<br/>
-      <a name="axtripleforproof1" id="axtripleforproof1"></a>rdfs:subClassOf rdfs:domain 
+      <a id="axtripleforproof1"></a>rdfs:subClassOf rdfs:domain 
       rdfs:Class .<br/>
       rdf:subject rdfs:domain rdf:Statement .<br/>
       rdf:predicate rdfs:domain rdf:Statement .<br/>
@@ -691,7 +691,7 @@
       rdfs:domain rdfs:range rdfs:Class .<br/>
       rdfs:range rdfs:range rdfs:Class .<br/>
       rdfs:subPropertyOf rdfs:range rdf:Property .<br/>
-      <a name="axtripleforproof2" id="axtripleforproof2"></a>rdfs:subClassOf rdfs:range 
+      <a id="axtripleforproof2"></a>rdfs:subClassOf rdfs:range 
       rdfs:Class .<br/>
       rdf:subject rdfs:range rdfs:Resource .<br/>
       rdf:predicate rdfs:range rdfs:Resource .<br/>
@@ -805,7 +805,7 @@
   entailments hold than held before the change. All of these additions are <a href="#glossMonotonic" class="termref"><em>monotonic</em></a>, 
   in the sense that entailments which hold before the addition of information, 
   also hold after it. We can sum up this in a single lemma:</p>
-<p ><strong><a name="GeneralMonotonicityLemma" id="GeneralMonotonicityLemma"></a>General monotonicity lemma</strong>. Suppose
+<p ><strong><a id="GeneralMonotonicityLemma"></a>General monotonicity lemma</strong>. Suppose
       that S, S' are sets of RDF graphs with every member of S  a subset
       of some member of S'. Suppose that Y indicates a semantic extension
       of&nbsp; X, S X-entails E, and   S and
@@ -824,7 +824,7 @@
   the following '<a class="termref" href="#glossExtensional">extensional</a>' 
   <div class="tabletitle">Extensional alternatives for some RDFS semantic conditions.</div>
-<table summary="range and domain extension conditions"  border="1">
+<table border="1">
     <td class="semantictable"> <p>&lt; x,y &gt; is in IEXT(I(<code>rdfs:subClassOf</code>)) 
         if and only if x and y are in IC and ICEXT(x) is a subset of ICEXT(y)</p></td>
@@ -882,10 +882,10 @@
   processes to check formal RDF entailment. For example, implementations may decide 
   to use special procedural techniques to implement the RDF collection vocabulary.</p>
-<h3><a name="Reif" id="Reif">Reification</a></h3>
+<h3><a id="Reif">Reification</a></h3>
     <div class="c1">  
-      <table  border="1" summary="reification vocabulary">
+      <table  border="1">
             <td class="othertable"><strong>RDF reification vocabulary</strong></td>
@@ -960,9 +960,9 @@
     <p><code>_:yyy &lt;ex:property&gt; &lt;ex:foo&gt; .</code></p>
-<h4><a name="Containers" id="Containers">RDF containers</a></h4>
+<h4><a id="Containers">RDF containers</a></h4>
-    <table border="1" summary="container vocabulary">
+    <table border="1">
           <td class="othertable"><strong>RDF Container Vocabulary</strong></td>
@@ -1056,9 +1056,9 @@
     only finitely many members.</p>
-<h4><a name="collections" id="collections"></a>RDF collections</h4>
+<h4><a id="collections"></a>RDF collections</h4>
-    <table  border="1" summary="collection vocabulary">
+    <table  border="1">
           <td class="othertable"><strong>RDF Collection Vocabulary</strong></td>
@@ -1140,7 +1140,7 @@
   the <code>rdf:rest</code> property, be of <code>rdf:type rdf:List</code>. </p>
-<h3><a name="rdfValue" id="rdfValue"></a>rdf:value</h3>
+<h3><a id="rdfValue"></a>rdf:value</h3>
 <p>The intended use for <code>rdf:value</code> is <a href="">explained 
   intuitively</a> in the RDF Primer
   document [[RDF-PRIMER]]. It is typically 
@@ -1169,7 +1169,7 @@
     which is claimed to be true. (ii) The act of claiming something to
     be true.</p>
-    <p><strong><a name="glossClass" id="glossClass"></a>Class</strong>
+    <p><strong><a id="glossClass"></a>Class</strong>
     (n.) A general concept, category or classification. Something<a
     href="#glossResource" class="termref"></a> used primarily to
     classify or categorize other things. Formally, in RDF, a <a
@@ -1204,7 +1204,7 @@
     the expression constructed from the <a href="#glossAntecedent"
     class="termref">antecedent</a>. In an entailment relation, the
     entailee. Also <em>conclusion</em>.</p>
-<p><strong><a name="glossConsistent" 
 	id="glossConsistent"></a>Consistent</strong> (adj., of an expression) Having 
   a satisfying <a href="#glossInterpretation"
     class="termref">interpretation</a>; not internally contradictory. (Also used 
@@ -1212,7 +1212,7 @@
 <p><strong><a name="glossCorrect"
     id="glossCorrect"></a>Correct</strong> (adj., of an inference system). Unable 
   to draw any invalid inferences, or unable to make false claims of entailment. See <em>Inference</em>.</p>
-<p><strong><a name="glossDecidable" id="glossDecidable"></a>Decidable</strong> 
+<p><strong><a id="glossDecidable"></a>Decidable</strong> 
   (adj., of an inference system). Able to determine for any pair of expressions, 
   in a finite time with finite resources, whether or not the first entails the 
   second. (Also: adj., of a logic:) Having a decidable inference system which 
@@ -1254,7 +1254,7 @@
     sufficiently precise as to enable results to be established using
     conventional mathematical techniques.</p>
-    <p><strong><a name="glossIff" id="glossIff"></a>Iff</strong>
+    <p><strong><a id="glossIff"></a>Iff</strong>
     (conj.) Conventional abbreviation for 'if and only if'. Used to
     express necessary and sufficient conditions.</p>
 <p><a name="glossInconsistent"
@@ -1316,7 +1316,7 @@
     semantics takes the simpler route of merging these into a single
-    <p><strong><a name="glossLogic" id="glossLogic"></a>Logic</strong>
+    <p><strong><a id="glossLogic"></a>Logic</strong>
     (n.) A formal language which expresses <a href="#glossProposition"
@@ -1395,7 +1395,7 @@
     propositions from the expressions which are used to state them, but
     model theory does not require this distinction.)</p>
-    <p><strong><a name="glossReify" id="glossReify"></a>Reify</strong>
+    <p><strong><a id="glossReify"></a>Reify</strong>
     (v.), <strong>reification</strong> (n.) To categorize as an object;
     to describe as an entity. Often used to describe a convention
     whereby a syntactic expression is treated as a semantic object and
@@ -1422,7 +1422,7 @@
     of meanings. Often contrasted with <em>syntactic</em> to emphasize
     the distinction between expressions and what they denote.</p>
-    <p><a name="glossSkolemization" id="glossSkolemization"></a><a
+    <p><a id="glossSkolemization"></a><a
     href="#skolemlemprf"><strong>Skolemization</strong></a> (n.) A
     syntactic transformation in which blank nodes are replaced by 'new'
@@ -1435,7 +1435,7 @@
     A. T. Skolem</a>)</p>
-    <p><a name="glossToken" id="glossToken"></a><strong>Token</strong>
+    <p><a id="glossToken"></a><strong>Token</strong>
     (n.) A particular physical inscription of a symbol or expression in
     a document. Usually contrasted with <em>type</em>, the abstract
     grammatical form of an expression.</p>
@@ -1446,7 +1446,7 @@
     things that an interpretation considers to exist. In RDF/S, this is
     identical to the set of resources.</p>
-    <p><strong><a name="glossUse" id="glossUse"></a>Use</strong> (v.)
+    <p><strong><a id="glossUse"></a>Use</strong> (v.)
     contrasted with <em>mention</em>; to use a piece of syntax to
     denote or refer to something else. The normal way that language is
@@ -1457,7 +1457,7 @@
-    <p><strong><a name="glossValid" id="glossValid"></a>Valid</strong>
+    <p><strong><a id="glossValid"></a>Valid</strong>
     (adj., of an inference or inference process) Corresponding to an <a
     href="#glossEntail" class="termref">entailment</a>, i.e. the
     conclusion of the inference is entailed by the antecedent of the
@@ -1466,7 +1466,7 @@
     <p><dfn>Well-formed</dfn> (adj., of an
     expression). Syntactically legal.</p>
-    <p><strong><a name="glossWorld" id="glossWorld"></a>World</strong>
+    <p><strong><a id="glossWorld"></a>World</strong>
     (n.) (with <em>the:</em>) (i) The actual world. (with
     <em>a:</em>) (ii) A way that the actual world might be arranged.
     (iii) An <a href="#glossInterpretation"