--- 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">
<tbody>
@@ -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">
<tbody>
@@ -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>
</section>
@@ -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">
<tbody>
<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)= < sss, ttt > </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">
<tbody>
<tr>
- <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 <x, I(<code>rdf:Property</code>)> is in IEXT(I(<code>rdf:type</code>))</td>
</tr>
-<tr><td class="semantictable"><a name="rdfsemcond3" id="rdfsemcond3">For every IRI aaa in D, < x, I(aaa) > 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, < x, I(aaa) > is in IEXT(I(<code>rdf:type</code>)) if and only if x is in the value space of I(aaa)</td></tr>
</tbody>
@@ -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">
<tr>
- <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">
<tbody>
<tr>
<td class="othertable"><strong>RDFS vocabulary</strong></td>
@@ -593,7 +593,7 @@
<table border="1">
<tr>
- <td class="semantictable"> <p><a name="rdfssemcond1" id="rdfssemcond1"></a>ICEXT(y) is defined to be { x : < x,y > is in IEXT(I(<code>rdf:type</code>)) }</p>
+ <td class="semantictable"> <p><a id="rdfssemcond1"></a>ICEXT(y) is defined to be { x : < x,y > 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 @@
</tr>
<tr>
- <td class="semantictable"> <p><a name="rdfssemcond2" id="rdfssemcond2"></a>If
+ <td class="semantictable"> <p><a id="rdfssemcond2"></a>If
< x,y > is in IEXT(I(<code>rdfs:domain</code>)) and < u,v > is
in IEXT(x) then u is in ICEXT(y)</p></td>
</tr>
<tr>
- <td class="semantictable"> <p><a name="rdfssemcond3" id="rdfssemcond3"></a>If
+ <td class="semantictable"> <p><a id="rdfssemcond3"></a>If
< x,y > is in IEXT(I(<code>rdfs:range</code>)) and < u,v > is
in IEXT(x) then v is in ICEXT(y)</p></td>
</tr>
<tr>
- <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>
</tr>
<tr>
- <td class="semantictable"> <p><a name="rdfssemcond5" id="rdfssemcond5"></a>If
+ <td class="semantictable"> <p><a id="rdfssemcond5"></a>If
<x,y> 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>
</tr>
<tr>
- <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 < x, I(<code>rdfs:Resource</code>) > is in IEXT(I(<code>rdfs:subClassOf</code>))</p></td>
</tr>
<tr>
- <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>
</tr>
- <td class="semantictable"> <p><a name="rdfssemcond7" id="rdfssemcond7"></a>If
+ <td class="semantictable"> <p><a id="rdfssemcond7"></a>If
< x,y > 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>
</tr>
@@ -644,14 +644,14 @@
<tr>
- <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/>
< x, I(<code>rdfs:member</code>) > is in IEXT(I(<code>rdfs:subPropertyOf</code>))<br/>
</p></td>
</tr>
<tr>
- <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 >< x,
I(<code>rdfs:Literal</code>) > is in IEXT(I(<code>rdfs:subClassOf</code>))</span></p></td>
</tr>
@@ -664,7 +664,7 @@
<p><a id="RDFS_axiomatic_triples" name="RDFS_axiomatic_triples"> </a>
</p>
<div class="tabletitle">RDFS axiomatic triples.</div>
- <table border="1" summary="RDFS axioms">
+ <table border="1">
<tr>
@@ -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 X, S X-entails E, and S and
@@ -824,7 +824,7 @@
the following '<a class="termref" href="#glossExtensional">extensional</a>'
versions:</p>
<div class="tabletitle">Extensional alternatives for some RDFS semantic conditions.</div>
-<table summary="range and domain extension conditions" border="1">
+<table border="1">
<tr>
<td class="semantictable"> <p>< x,y > 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">
<tbody>
<tr>
<td class="othertable"><strong>RDF reification vocabulary</strong></td>
@@ -960,9 +960,9 @@
<p><code>_:yyy <ex:property> <ex:foo> .</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">
<tbody>
<tr>
<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">
<tbody>
<tr>
<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="http://www.w3.org/TR/rdf-primer/#rdfvalue">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"
+<p><strong><a
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
concept.)</p>
- <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"
class="termref">propositions</a>.</p>
@@ -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'
names.</p>
@@ -1435,7 +1435,7 @@
href="http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Skolem.html">
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
used.</p>
@@ -1457,7 +1457,7 @@
href="http://www.philosophypages.com/dy/t.htm">Alfred
Tarski</a>)</p>
- <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"