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Properties of simple entailment and satisfiability

If E contains an IRI which does not occur anywhere in S, then S does not simply entail E.

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The following semantic properties relate triple terms and triples asserted in a graph, and they introduce a general definition of satisfiability.

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The following semantic properties relate triple terms, triples asserted in a graph and reified triples, and they introduce a general definition of satisfiability.

We define the set of propositions in an interpretation as follows:

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Properties of simple entailment and satisfiability

The set F of facts in an interpretation I is F(I) = { RE(x, y, z)|<x, z> is in IEXT(y) }. The set of facts is the set of propositions which are true in the interpretation.

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We define the set of reifications in an interpretation as follows:

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The set R of reifications in an interpretation I is R(I) = { RE(x, y, z)| + x is in IR, + y is rdf:reifies, + z is a triple term and + <x, z> is in IEXT(y) }. + The set of reifications is the multi-set of propositions which are reified in an 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) = { RE( [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.

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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.

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RDF reification, containers and collections

processes to check formal RDF entailment. For example, implementations may decide to use special procedural techniques to implement the RDF collection vocabulary.

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RDF 1.2 reification - triple terms and reifiers

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+ To repeat nomenclatura: +

. + + Reifying an abstract proposition, encoded as a triple term, + never entails that triple as a fact. + Neither does a fact entail a reification of that triple. + + From that follows that in a strict interpretation of the model-theoretic semantics of RDF 1.2 + an assertion on a reified triple (denoted by a reifier) + can never be an assertion on a fact asserting that same triple. + The connection between a reification and an assertion of the same triple, + even if they occur in the same graph, + can only be understood as being merely coincidental. + + A looser interpretation of that connection + as one of identification, + not denotation, + as applied in RDF 1.2 Concepts, RDF 1.2 Primer and the RDF 1.2 note on triple terms (tbd), + establishes an operational semantics of such a connection between reification and fact + as convention and best practice. + The semantics of RDF 1.2's triple term-based reification mechanism thus diverges + from RDF 1.0/1.1 reification which strictly upholds the model-theoretic interpretation + that reified and asserted triple have no connection beyond mere coincidence. + This design was chosen to facilitate assertions on asserted triples, a.k.a. "statements about statements", + while keeping the model-theoretic semantics of RDF 1.2 simple + and upholding a safe distance from modal logic complications. +

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Reification

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RDF 1.0/1.1 reification - statement quad reification