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Re: Expressiveness of RDF as Rule Conclusion Language (was Re: W hat is an RDF Query? )

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Fri, 12 Oct 2001 09:29:57 -0400 (EDT)
Message-Id: <200110121329.f9CDTvG27705@pantheon-po02.its.yale.edu>
To: www-rdf-rules@w3.org

   [Gerd Wagner]
   Notice that we can associate a model-theoretic semantics with rules 
   in a natural way: an interpretation I satisfies a rule (is a model
   of it) if it satisfies its consequent whenever it satisfies its 
   antecedcent. 

   > >The sentence (status-known Joe) could also be inferred from the
   > >two rules alone,
   > 
   [Pat Hayes]
   > From the two implications, but not from the rules. In fact, strictly 
   > speaking, nothing can be inferred *from* a rule, only *by* a rule.

   Yes, we can infer from a rule set: using the above definition of a
   model of a rule, we can define that a rule set R entails a sentence F 
   if all models of R satisfy F (in logic programming we say that 
   R entails F if all stable models of R satisfy F).

You're assuming that a what a rule set entails by your definition is
equivalent to what is inferrable.  That is, you're assuming that the
theory + rules is complete.  But the sort of rule in question here
gives rise to incompleteness for precisely the reasons you describe:
'(status-known Joe)' is true in all models, but can't be inferred.
This may be an argument against your proposed model-theoretic
semantics for rules.

                                             -- Drew McDermott
Received on Friday, 12 October 2001 09:30:00 GMT

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