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"no-semantics" semantics

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 18 Sep 2012 00:56:27 -0500
Message-Id: <89650BC3-1B4B-48E8-B489-8BB2F63396F0@ihmc.us>
To: RDF WG <public-rdf-wg@w3.org>
<summary> The "RDF no-semantics" proposal does not make sense as written, and I do not think that it makes sense at all. If part of the current proposal depends upon the use of a semantics weaker than simple entailment, then it needs to be reconsidered. </summary>

According to http://www.w3.org/2011/rdf-wg/wiki/TF-Graphs/Dataset-semantics-2.0#RDF_no-semantics, the no-semantics semantic condition is:  

I(G)=true if IR contains (an RDF graph isomorphic to) G. 

This does not really make any sense. Why would the presence of an object (of any kind) in the universe cause a graph to be true? This does not bear any relationship to the truth of the triples in the graph or the denotations of the URIs in the graph.  Notice that this would give the same entailments if any other part of the semantic conditions were required to contain G, for example if we were to say that i(G)=true if for some IRI R  in a triple in G, I(R)=G, or that I(G)=true if IP contains G. All that matters is that the 'truth' of G is defined so that the interpretation structure is required to contain G, and then entailment holds only for identity (or isomorphism) of the graph, trivially. But this 'tricks' the standard notion of truth to achieve the weaker entailment, and this trickery has the consequence that the usual notions of entailment are no longer strengthenings of this one.

There is a standard way to relate a stronger notion of entailment to a weaker one, which is used extensively in the 2004 RDF semantics. One does it by restricting the class of possible interpretations. A entails B means that every interpretation which makes A true also makes B true. The more interpretations one allows in that "every", the weaker the entailement. So one gets RDF entailment from simple entailment by only allowing RDF interpretations (that is, simple interpretations which satisfy the RDF semantic conditions), and RDFS from RDF by only allowing RDFS interpretations, and so on. This is basic textbook stuff, model theory 101. But this does not work for this trick. A simple RDF interpretation is not a no-semantics interpretation with extra conditions added. The two kinds of interpretation bear essentially no relationship to one another: the "no-semantics" truth conditions are completely unrelated to the normal truth conditions, and the simple interpretation is not required to contain a graph in its universe. 

This trick also violates the basic intuitions underlying model theoretic semantics. The whole idea is to define the truth of complex expressions in terms of the semantic values of their subexpressions. In logic, for example, the truth of a sentence like (forall (x)(if (and (P x)(Q x)) (P x)))  is defined in terms of the denotations of (if (and (P x)(Q x)) (P x)), which in turn is defined in terms of the truth of  (and (P x)(Q x)) and of (P x), and so on. The "no-semantics" semantics does not do this. 

I am not willing to include this option as a part of a standard semantics document authored by me.


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Received on Tuesday, 18 September 2012 05:56:59 UTC

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