Re-wording the semantics

Let me suggest some re-wording for the model theory and "basics". This just brings everything more into line with the way things are expressed in the current semantics, and is a little more precise. 

1.2 Model-theoretic semantics

Let E be an entailment regime and V a vocabulary. An E-ds-interpretation of V is an E-interpretation of V together with a function IGEXT from the universe of I to the set of RDF graphs. 

For a pair <n, G>, I(<n, G>) is true iff IGEXT(ID(n)) E-entails G;
For a dataset D= {DG, <n1,G1>,…,<nk,Gk>), I(D) is true iff I(DG) is true and for all i in 1…k, I(<ni,Gi>) is true.

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Notice that with this way of phrasing the model theory, it is automatic that a dataset interpretation is also a graph interpretation. The extra structure is simply ignored when we are considering the truth of a graph in the interpretation. 

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2.1 Basics (standard definitions)

A E-entails B when for every E-ds-interpretation which makes A true also makes B true. 
A is E-equivalent to B when A E-entails B and B E-entails A.
A is an E-contradiction when A is false in every E-interpretation.





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Received on Thursday, 13 September 2012 04:55:50 UTC