--- a/rdf-mt/index.html Mon Apr 01 16:14:29 2013 +0200
+++ b/rdf-mt/index.html Mon Apr 01 16:53:42 2013 +0200
@@ -449,7 +449,7 @@
<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>
-</tbody></table></p>
+</tbody></table>
<p>If the literal is ill-typed then the L2V 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 ill-typed literal will be D-inconsistent, i.e. false in every D-interpretation. This applies only to datatype IRIs in D; literals with "unknown" datatypes are not ill-typed and do not produce a D-inconsistency. </p>
@@ -493,7 +493,7 @@
<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 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)</a></td></tr>
</tbody>
@@ -516,7 +516,7 @@
... <br/>
</code>
- </code></td>
+ </td>
</tr>
</table>
@@ -542,12 +542,10 @@
<code>aaa ppp _:x . <br/> _:x rdf:type xsd:integer .</code>
-</p>
-
</section>
<section><h2>RDFS Interpretations and RDFS entailment</h2>
<p>RDF Schema [<cite><a href="#ref-rdf-vocabulary">RDF-VOCABULARY</a></cite>]
- extends RDF to a larger <a id="defRDFSV" name="defRDFSV"></a>vocabulary
+ extends RDF to a larger <a id="defRDFSV"></a>vocabulary
with more complex semantic constraints:</p>
<div class="c1">
@@ -585,7 +583,7 @@
</p>
-<p><a id="rdfsinterpdef" name="rdfsinterpdef"></a> An <i>rdfs-D-interpretation</i> is an <a href="#rdfinterpdef" class="termref">rdf-D-interpretation</a> I
+<p><a id="rdfsinterpdef"></a> An <i>rdfs-D-interpretation</i> is an <a href="#rdfinterpdef" class="termref">rdf-D-interpretation</a> I
which satisfies the semantic conditions in the following table, and satisfies all the triples in the subsequent table of <em>RDFS axiomatic triples</em>. As before, an <em>rdfs-interpretation</em>, or <em>RDFS interpretation</em>, is an rdfs-D-interpretation with D= {<code>xsd:string</code>, <code>rdf:langString</code> }.</p>
<p class="issue">This table has redundancies. I am inclined to leave them alone, as it takes quite a lot of thought to figure out some of the consequences when we only give non-redundant conditions. </p>
@@ -636,7 +634,8 @@
is transitive and reflexive on IC</p></td>
</tr>
- <td class="semantictable"> <p><a id="rdfssemcond7"></a>If
+ <tr>
+ <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>
@@ -661,7 +660,7 @@
- <p><a id="RDFS_axiomatic_triples" name="RDFS_axiomatic_triples"> </a>
+ <p><a id="RDFS_axiomatic_triples"> </a>
</p>
<div class="tabletitle">RDFS axiomatic triples.</div>
<table border="1">
@@ -852,7 +851,7 @@
in the main text provides for most common uses of subclass and subproperty assertions,
and allows for simpler implementations of a <a href="#glossComplete" class="termref">
complete</a> set of RDFS entailment rules, described in <a href="#RDFSRules" class="termref"> ////</a>.</p>
-</li><ul>
+</li></ul>
</section>
@@ -1135,7 +1134,7 @@
values of the items, in the order got by tracing the <code>rdf:rest</code> properties
from the subject to <code>rdf:nil</code>. This permits sequences which contain
other sequences.</p>
-<p The RDFS semantic conditions require that any
+<p> The RDFS semantic conditions require that any
subject of the <code>rdf:first</code> property, and any subject or object of
the <code>rdf:rest</code> property, be of <code>rdf:type rdf:List</code>. </p>
@@ -1150,13 +1149,13 @@
<p>Since the range of possible uses for <code>rdf:value</code> is so wide, it
is difficult to give a precise statement which covers all the intended meanings
or use cases. Users are cautioned, therefore, that the
- meaning of <code>rdf:value</code> may vary from application to application</span>.
+ meaning of <code>rdf:value</code> may vary from application to application.
Even when the intended meaning is clear from the context in the original graph document, it may be
lost when graphs are merged or when conclusions are inferred.</p>
</section>
<section class="appendix" id="glossary"><h2>Glossary of Terms (Informative)</h2>
- <p><strong><a name="glossAntecedent"
+ <p><strong><a
id="glossAntecedent"></a>Antecedent</strong> (n.) In an <a
href="#glossInference" class="termref">inference</a>, the
expression(s) from which the <a href="#glossConsequent"
@@ -1164,8 +1163,7 @@
href="#glossEntail" class="termref">entailment</a> relation, the
entailer. Also <em>assumption</em>.</p>
- <p><strong><a name="glossAssertion"
- id="glossAssertion"></a>Assertion</strong> (n.) (i) Any expression
+ <p><strong><a id="glossAssertion"></a>Assertion</strong> (n.) (i) Any expression
which is claimed to be true. (ii) The act of claiming something to
be true.</p>
@@ -1183,7 +1181,7 @@
<p>(RDF distinguishes <em>class</em> from <em>set</em>, although the two are often
identified. Distinguishing classes from sets allows RDF more
freedom in constructing class hierarchies.</p>
-<p><strong><a name="glossComplete"
+<p><strong><a
id="glossComplete"></a>Complete</strong> (adj., of an inference system). (1)
Able to detect all <a
href="#glossEntail" class="termref">entailment</a>s between any two expressions.
@@ -1199,7 +1197,7 @@
mechanical inference systems may be complete in the first sense but not necessarily
in the second.) </p>
- <p><strong><a name="glossConsequent"
+ <p><strong><a
id="glossConsequent"></a>Consequent</strong> (n.) In an inference,
the expression constructed from the <a href="#glossAntecedent"
class="termref">antecedent</a>. In an entailment relation, the
@@ -1209,7 +1207,7 @@
a satisfying <a href="#glossInterpretation"
class="termref">interpretation</a>; not internally contradictory. (Also used
of an inference system as synonym for <em>Correct</em>.) </p>
-<p><strong><a name="glossCorrect"
+<p><strong><a
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 id="glossDecidable"></a>Decidable</strong>
@@ -1222,8 +1220,7 @@
The relationships between logical syntax, semantics and complexity of an inference
system continue to be the subject of considerable research.)</p>
- <p><strong><a name="glossEntail"
- id="glossEntail"></a>Entail</strong> (v.),
+ <p><strong><a id="glossEntail"></a>Entail</strong> (v.),
<strong>entailment</strong> (n.). A semantic relationship between
expressions which holds whenever the truth of the first guarantees
the truth of the second. Equivalently, whenever it is logically
@@ -1233,15 +1230,13 @@
class="termref">satisfies</a> the first also satisfies the second.
(Also used between a set of expressions and an expression.)</p>
- <p><strong><a name="glossEquivalent"
- id="glossEquivalent"></a>Equivalent</strong> (prep., with
+ <p><strong><a id="glossEquivalent"></a>Equivalent</strong> (prep., with
<em>to</em>) True under exactly the same conditions; making
identical claims about the world, when asserted. <a
href="#glossEntail" class="termref">Entails</a> and is entailed
by.</p>
- <p><strong><a name="glossExtensional"
- id="glossExtensional"></a>Extensional</strong> (adj., of a logic) A
+ <p><strong><a id="glossExtensional"></a>Extensional</strong> (adj., of a logic) A
set-based theory or logic of classes, in which classes are
considered to be sets, properties considered to be sets of
<object, value> pairs, and so on. A theory which admits no
@@ -1249,7 +1244,7 @@
href="#glossIntensional"
class="termref"><em>Intensional</em></a>.</p>
- <p><strong><a name="glossFormal"
+ <p><strong><a
id="glossFormal"></a>Formal</strong> (adj.) Couched in language
sufficiently precise as to enable results to be established using
conventional mathematical techniques.</p>
@@ -1257,7 +1252,7 @@
<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"
+<p><a
id="glossInconsistent"></a><strong>Inconsistent</strong> (adj.) False under
all interpretations; impossible to <a
href="#glossSatisfy" class="termref">satisfy</a>. <strong>Inconsistency</strong>
@@ -1273,11 +1268,11 @@
often harder to detect consistency in all cases than to detect inconsistency
in all cases<a
href="#glossEntail" class="termref"></a>.)</p>
-<p><strong><a name="glossIndexical"
+<p><strong><a
id="glossIndexical"></a>Indexical</strong> (adj., of an expression) having
a meaning which implicitly refers to the context of use. Examples from English
include words like 'here', 'now', 'this'.</p>
-<p><strong><a name="glossInference"
+<p><strong><a
id="glossInference"></a>Infer</strong><strong>ence</strong> (n.) An act or
process of constructing new expressions from existing expressions, or the result
of such an act or process. Inferences corresponding to <a href="#glossEntail"
@@ -1286,7 +1281,7 @@
<strong>inference system</strong>, organized system of inference rules; also,
software which generates inferences or checks inferences for validity.</p>
- <p><strong><a name="glossIntensional"
+ <p><strong><a
id="glossIntensional"></a>Intensional</strong> (adj., of a logic)
Not <a href="#glossExtensional" class="termref">extensional</a>. A
logic which allows distinct entities with the same extension.</p>
@@ -1302,7 +1297,7 @@
have the same instances, such as human beings and bipedal hominids without body
hair. The semantics described in this document is basically intensional.)</p>
- <p><strong><a name="glossInterpretation"
+ <p><strong><a
id="glossInterpretation"></a>Interpretation</strong>
(<strong>of</strong>) (n.) A minimal formal description of those
aspects of a <a href="#glossWorld" class="termref">world</a> which
@@ -1320,12 +1315,12 @@
(n.) A formal language which expresses <a href="#glossProposition"
class="termref">propositions</a>.</p>
- <p><a name="glossMetaphysical"
+ <p><a
id="glossMetaphysical"></a><strong>Metaphysical</strong> (adj.).
Concerned with the true nature of things in some absolute or
fundamental sense.</p>
- <p><a name="glossModeltheory"
+ <p><a
id="glossModeltheory"></a><strong>Model Theory</strong> (n.) A
formal semantic theory which relates expressions to
interpretations.</p>
@@ -1337,7 +1332,7 @@
"computational modelling", so has been avoided in this
document.)</p>
- <p><strong><a name="glossMonotonic"
+ <p><strong><a
id="glossMonotonic"></a>Monotonic</strong> (adj., of a logic or
inference system) Satisfying the condition that if S entails E then
(S + T) entails E, i.e. adding information to some antecedents
@@ -1351,7 +1346,7 @@
class="termref">valid</a> outside of the context in which they were
generated. This is why RDF is designed to be monotonic.)</p>
- <p><strong><a name="glossNonmonotonic"
+ <p><strong><a
id="glossNonmonotonic"></a>Nonmonotonic</strong> (adj.,of a logic
or inference system) Not <a href="#glossMonotonic"
class="termref">monotonic</a>. Non-monotonic formalisms have been
@@ -1380,13 +1375,13 @@
Making the context explicit in the reasoning and visible in the
conclusion is a way to map them into a monotonic framework.)</p>
- <p><strong><a name="glossOntological"
+ <p><strong><a
id="glossOntological"></a>Ontological</strong> (adj.) (Philosophy)
Concerned with what kinds of things really exist. (Applied)
Concerned with the details of a formal description of some topic or
domain.</p>
- <p><strong><a name="glossProposition"
+ <p><strong><a
id="glossProposition"></a>Proposition</strong> (n.) Something that
has a truth-value; a statement or expression that is true or
false.</p>
@@ -1402,12 +1397,12 @@
itself described using another syntax. In RDF, a reified triple is
a description of a triple-token using other RDF triples.</p>
- <p><strong><a name="glossResource"
+ <p><strong><a
id="glossResource"></a>Resource</strong> (n.)(as used in RDF)(i) An
entity; anything in the universe. (ii) As a class name: the class
of everything; the most inclusive category possible.</p>
- <p><strong><a name="glossSatisfy"
+ <p><strong><a
id="glossSatisfy"></a>Satisfy</strong> (v.t.),
<strong>satisfaction</strong>,(n.) <strong>satisfying</strong>
(adj., of an interpretation). To make true. The basic semantic
@@ -1416,7 +1411,7 @@
world</a> conforms to the conditions described by X, then Y must be
true.</p>
- <p><strong><a name="glossSemantic"
+ <p><strong><a
id="glossSemantic"></a>Semantic</strong> (adj.) ,
<strong>semantics</strong> (n.). Concerned with the specification
of meanings. Often contrasted with <em>syntactic</em> to emphasize
@@ -1440,7 +1435,7 @@
a document. Usually contrasted with <em>type</em>, the abstract
grammatical form of an expression.</p>
- <p><strong><a name="glossUniverse"
+ <p><strong><a
id="glossUniverse"></a>Universe</strong> (n., also <em>Universe of
discourse</em>) The universal classification, or the set of all
things that an interpretation considers to exist. In RDF/S, this is