We observe that no IRI, not even those in the rdf: namespace,
+ has any special semantic condition associated with it in a simple interpretation.
Semantic extensions may impose further constraints upon interpretation mappings by requiring some IRIs to denote in particular ways. @@ -722,19 +724,36 @@
We define the set of propositions in an interpretation as follows:
- The set of propositions in an interpretation I is IPR(I) = { IT(x, y, z)｜x is in IR, y is in IP, z is in IR }; we observe that a proposition is in the extension of rdfs:Proposition.
The set of propositions in an interpretation I is + IPR(I) = { IT(x, y, z) ｜ x is in IR, + y is in IP, z is in IR }.
+ +The denotation of a triple is a proposition, whether it is used as a triple
+ term or an asserted triple. Under RDFS
+ Interpretations (see below), a proposition is in the extension of the
+ class rdfs:Proposition.
We define the set of facts in an interpretation as follows:
-The set F of facts in an interpretation I is F(I) = { IT(x, y, z)｜<x, z> is in IEXT(y) }. The set of facts is the set of propositions which are true in the interpretation.
+The set F of facts in an interpretation I is F(I) = { IT(x, y, z)｜<x, z> is in IEXT(y) }.
+ +A fact in an interpretation is a proposition that holds in it, corresponding to a triple which is true in that interpretation.
Given a blank node mapping, we define the set of facts asserted by a graph in an interpretation as follows:
-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) = { IT( [I+A](s), I(p), [I+A](o) )｜`s p o.` is in G }. 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.
+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) = { IT( [I+A](s), I(p), [I+A](o) )｜ + `s p o.` is in G }.
-We introduce a general definition of satisfiability of a graph in an interpretation as follows:
- -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.
+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. + Intuitively, this would only be the case if the interpretation satisfies the graph. +
+ +An interpretation I (simply) satisfies a graph G + if and only if there exists a blank node mapping A such that the facts + asserted by the graph in the interpretation FEXT(G,I,A) are a subset of + the facts of the interpretation F(I).
@@ -1243,9 +1262,18 @@ A class may have an
empty class extension. Two different classes can have the same class extension.
The class extension of rdfs:Class contains the class rdfs:Class.
An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I - which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.
+ +RDFS also introduces the class rdfs:Proposition,
+ whose extension is exactly the set of propositions as defined
+ in [[[#simple_entailment_properties]]].
+ This class is also declared as `rdfs:range` of the `rdf:reifies` property.
+ In other words, the object of a reifying triple
+ always denotes a proposition.
+
+
An RDFS interpretation (recognizing D) is an + RDF interpretation (recognizing D) I which satisfies the + semantic conditions in the following table, and all the triples in the + subsequent table of RDFS axiomatic triples.