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Re-wording the semantics

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 12 Sep 2012 23:55:16 -0500
Message-Id: <CF86625A-58B5-4937-9CEA-3C07135E8D76@ihmc.us>
Cc: RDF Working Group <public-rdf-wg@w3.org>
To: Antoine Zimmermann <antoine.zimmermann@emse.fr>
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 1k, I(<ni,Gi>) is true.


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. 


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

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