From: Wagner, G.R. <G.R.Wagner@tm.tue.nl>

Date: Thu, 5 Sep 2002 19:17:21 +0200

Message-ID: <AA2E843B3FC96349BF60350202650BE92571D2@tmex1.tm.tue.nl>

To: "'Peter F. Patel-Schneider'" <pfps@research.bell-labs.com>, sandro@w3.org

Cc: www-rdf-rules@w3.org, timbl@w3.org

Date: Thu, 5 Sep 2002 19:17:21 +0200

Message-ID: <AA2E843B3FC96349BF60350202650BE92571D2@tmex1.tm.tue.nl>

To: "'Peter F. Patel-Schneider'" <pfps@research.bell-labs.com>, sandro@w3.org

Cc: www-rdf-rules@w3.org, timbl@w3.org

> On the other hand > > a > --- > b > > is a different rule of inference, which should be read as > ``If you have concluded a then you can conclude b.'' This is, of course, not a rule of inference in the normal sense of a valid inference pattern (justified by the fact that all models of the premise satisfy the conclusion). We better call it a "material rule" or a "derivation rule". There is a type of logical formalism, sequent calculi, where such rules are called "sequents". >> A logical reasoner knowing one particular rule (which I think is >> "modus ponens": A, A->B |- A) will do the same thing given "p->q" as a >> rules engine would if it were given "p |- q". In fact, a reasoner >> using any other sound and sufficiently-complete set of inference rules > > would act the same given "p->q" as a rules engine would with "p |- q". > > This is definitely not true. A rules engine with p |- q will not conclude > anything from not q whereas a complete reasoner for the propositional > calculus will conclude not a from not b and a implies b. I disagree. Sandro is right. The models of the sequent "p |- q" are exactly the same models as those of the corresponding implication "p->q", so both expressions entail the same logical consequences according to their model-theoretic semantics - at least in standard logics such as classical and intuitionistic logic. But, and here comes the but, not so in certain nonmonotonic logics, such as the logic underlying normal logic programs (with negation-as-failure). See also the discussion in http://lists.w3.org/Archives/Public/www-rdf-rules/2001Oct/0025.html. -Gerd http://tmitwww.tm.tue.nl/staff/gwagnerReceived on Thursday, 5 September 2002 13:17:34 UTC

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