Skip to content

Commit 2ecb405

Browse files
franconipchampinniklaslafsTallTed
authored
Better text in Section 5.3 with the purpose of relating triple terms and asserted triples. (#156)
* Better text in Section 5.3 on propositions, facts, and asserted facts. * Added rdfs:Proposition explanation in RDFS Section * Added comment on rdf:reifies having no semantic condition in RDF * accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin <github-100614@champin.net> * accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin <github-100614@champin.net> * accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin <github-100614@champin.net> * accepted P-A improvement in text Co-authored-by: Pierre-Antoine Champin <github-100614@champin.net> * accepted Niklas text improvement Co-authored-by: Niklas Lindström <lindstream@gmail.com> * accepting Niklas amended text Co-authored-by: Niklas Lindström <lindstream@gmail.com> * accepted Andy's suggestion Co-authored-by: Andy Seaborne <andy@apache.org> * Added a brief intro on rdf:reifies * Block commit of all the suggestion until 10 September * Applied @TallTed suggestion Co-authored-by: Ted Thibodeau Jr <tthibodeau@openlinksw.com> --------- Co-authored-by: Pierre-Antoine Champin <github-100614@champin.net> Co-authored-by: Niklas Lindström <lindstream@gmail.com> Co-authored-by: Andy Seaborne <andy@apache.org> Co-authored-by: Ted Thibodeau Jr <tthibodeau@openlinksw.com>
1 parent 6639a2a commit 2ecb405

File tree

1 file changed

+37
-9
lines changed

1 file changed

+37
-9
lines changed

‎spec/index.html‎

Lines changed: 37 additions & 9 deletions
Original file line numberDiff line numberDiff line change
@@ -504,6 +504,8 @@ <h2>Simple Interpretations</h2>
504504
the referent of the subject and object of any true triple will be in IR;
505505
so any IRI which occurs in a graph both as a predicate and as a subject or object
506506
will denote something in the intersection of IP and IR.</p>
507+
<p>We observe that no IRI, not even those in the <code>rdf:</code> namespace,
508+
has any special semantic condition associated with it in a simple interpretation.</p>
507509

508510
<p><a>Semantic extensions</a> may impose further constraints upon interpretation mappings
509511
by requiring some IRIs to denote in particular ways.
@@ -722,19 +724,36 @@ <h3>Properties of simple entailment and satisfiability</h3>
722724

723725
<p>We define the <dfn>set of propositions</dfn> in an interpretation as follows:</p>
724726

725-
<p class="fact"> The set of propositions in an interpretation I is IPR(I) = {&nbsp;IT(x, y, z)&#65372;x is in IR, y is in IP, z is in IR&nbsp;}; we observe that a proposition is in the extension of <code>rdfs:Proposition</code>. </p>
727+
<p class="fact"> The set of propositions in an interpretation I is
728+
IPR(I)&nbsp;= {&nbsp;IT(x, y, z)&nbsp;&#65372;&nbsp;x&nbsp;is in IR,
729+
y&nbsp;is in IP, z&nbsp;is in IR&nbsp;}.</p>
730+
731+
<p>The denotation of a triple is a proposition, whether it is used as a triple
732+
term or an asserted triple. Under <a href="#rdfs_interpretations">RDFS
733+
Interpretations</a> (see below), a proposition is in the extension of the
734+
class <code>rdfs:Proposition</code>.</p>
726735

727736
<p>We define the <dfn>set of facts</dfn> in an interpretation as follows:</p>
728737

729-
<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;IT(x, y, z)&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}. The set of facts is the set of propositions which are true in the interpretation. </p>
738+
<p class="fact"> The set F of facts in an interpretation I is F(I) = {&nbsp;IT(x, y, z)&#65372;&lt;x, z&gt; is in IEXT(y)&nbsp;}. </p>
739+
740+
<p>A fact in an interpretation is a proposition that holds in it, corresponding to a triple which is true in that interpretation.</p>
730741

731742
<p>Given a blank node mapping, we define the <dfn>set of facts asserted by a graph</dfn> in an interpretation as follows:</p>
732743

733-
<p class="fact">Given a blank node mapping A, the set of all facts asserted by a graph G in an interpretation I is FEXT(G, I, A) = {&nbsp;IT(&nbsp;[I+A](s), I(p), [I+A](o)&nbsp;)&#65372;`s p o.` is in G&nbsp;}. We then observe that given a blank node mapping, the asserted facts of a graph with respect to an interpretation may not necessarily be among the facts of the interpretation.</p>
744+
<p class="fact">Given a blank node mapping&nbsp;A, the set of all facts
745+
asserted by a graph&nbsp;G in an interpretation&nbsp;I is FEXT(G, I,
746+
A)&nbsp;= {&nbsp;IT(&nbsp;[I+A](s), I(p), [I+A](o)&nbsp;)&#65372;
747+
`s p o.`&nbsp;is in G&nbsp;}.</p>
734748

735-
<p>We introduce a <dfn>general definition of satisfiability</dfn> of a graph in an interpretation as follows:</p>
736-
737-
<p class="fact">An interpretation (simply) satisfies a graph if and only if there exists a blank node mapping such that the facts asserted by the graph in the interpretation are among the facts of the interpretation.</p>
749+
<p>Given a blank node mapping and an interpretation, an asserted fact in a graph is the proposition corresponding to the denotation of a triple in the graph. These asserted facts may not necessarily be among the facts in the interpretation.
750+
Intuitively, this would only be the case if the interpretation satisfies the graph.
751+
</p>
752+
753+
<p class="fact">An interpretation&nbsp;I (simply) <a>satisfies</a> a graph&nbsp;G
754+
if and only if there exists a blank node mapping&nbsp;A such that the facts
755+
asserted by the graph in the interpretation&nbsp;FEXT(G,I,A) are a subset of
756+
the facts of the interpretation&nbsp;F(I).</p>
738757

739758
</section>
740759
</section>
@@ -1243,9 +1262,18 @@ <h2>RDFS Interpretations</h2>
12431262
<em>Ext</em>ension in I) from IC to the set of subsets of IR.</p><p> A class may have an
12441263
empty class extension. Two different classes can have the same class extension.
12451264
The class extension of <code>rdfs:Class</code> contains the class <code>rdfs:Class</code>.</p>
1246-
1247-
<p> An <dfn>RDFS interpretation</dfn> (<strong>recognizing D</strong>) is an <a>RDF interpretation</a> (recognizing D) I
1248-
which <a>satisfies</a> the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.</p>
1265+
1266+
<p>RDFS also introduces the class <code>rdfs:Proposition</code>,
1267+
whose extension is exactly the <a>set of propositions</a> as defined
1268+
in [[[#simple_entailment_properties]]].
1269+
This class is also declared as `rdfs:range` of the `rdf:reifies` property.
1270+
In other words, the object of a <a data-cite="RDF12-CONCEPTS#dfn-reifying-triple">reifying triple</a>
1271+
always denotes a <a data-cite="RDF12-CONCEPTS#dfn-proposition">proposition</a>.
1272+
1273+
<p> An <dfn>RDFS interpretation</dfn> (<strong>recognizing D</strong>) is an
1274+
<a>RDF interpretation</a> (recognizing D)&nbsp;I which <a>satisfies</a> the
1275+
semantic conditions in the following table, and all the triples in the
1276+
subsequent table of RDFS axiomatic triples.</p>
12491277

12501278
<table id="rdfs_semantic_conditions">
12511279
<caption>RDFS semantic conditions.</caption>

0 commit comments

Comments
 (0)