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RE: Is n3 a rules language or a logic language?

From: Wagner, G.R. <G.R.Wagner@tm.tue.nl>
Date: Wed, 11 Dec 2002 12:35:14 +0100
Message-ID: <AA2E843B3FC96349BF60350202650BE9257387@tmex1.tm.tue.nl>
To: "'pat hayes'" <phayes@ai.uwf.edu>
Cc: www-rdf-rules@w3.org

> Other proof systems can be goal-oriented, and in these cases the 
> deduction theorem would be incorrect.

No matter how proofs are established, the proof system defines 
a provability relation (which normally corresponds to the 
entailment relation), and the deduction theorem refers to this 
*relation*, and not to the procedure. 

> >In fact, this relationship between genuine implication
> >and entailment shows that implication is the most sophisticated
> >connective: it captures/reflects entailment in the object language!
> 
> That is a very misleading way to phrase it, in my view. If this were 
> correct then the deduction theorem would be trivial, but in fact in 
> many classical systems it is quite hard to prove.
 
In a constructive approach to logic, the (idea of the) deduction
theorem is the basis for introducing implication. In a more classical
(axiomatic) approach it has to be proved.

-Gerd
Received on Wednesday, 11 December 2002 07:00:51 GMT

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