Re: about "strong" negation

See also the work of Gerd, a RIFer among us:

Gerd Wagner: Logic Programming with Strong Negation and Inexact Predicates. Journal 
of Logic and Computation 1(6), 835-859 (1991)

David Pearce, Gerd Wagner: Logic Programming with Strong Negation. Peter 
Schroeder-Heister (Ed.): Extensions of Logic Programming, International Workshop, 
Tübingen, Germany, December 8-10, 1989, Proceedings. Lecture Notes in Computer 
Science 475 Springer, 311-326.

-hak

Axel Polleres wrote:
> 
> This quotes [1]:
> 
> Strong negation, representing constructible falsity, was introduced into
> logic by David Nelson. It was quickly popularised in Russia through the
> lectures and publications of A. A. Markov and subsequently axiomatised
> by N. N. Vorob’ev. In the 1950s, Nelson’s constructive logic with strong
> negation was studied in Warsaw by Rasiowa’s group using algebraic
> methods; the main results were later reproduced in ....
> 
> In principle strong negation can equivalently emulated in logic programs
> (under the Answer Set semantics, which is en extension of stable model
> semantics by (among others) strong negation) by:
> 
> Replacing each strongly negated atom -p(t1,...tn) to
> p'(t1,...tn) and adding axiomatic integrity constraints:
> 
> :- p(t1,...tn), p'(t1,...tn).
> 
> which prohibit that p(t1,...tn) and p'(t1,...tn) are both true in the
> same model.
> 
> Strong negation was introduced in this form by Gelfond and Lifschitz to
> the stable model semantics in their seminal paper [2] where they call it
> "classical" negation, which is a bit confusing, since, as I mentioned it
> does note have certain "features" of classical negation such as the law
> of the excluded middle for example.
> 
> best,
> axel
> 
> 1. David Pearce, Agustín Valverde. A First Order Nonmonotonic Extension
> of Constructive Logic. Studia Logica, Volume 80, Numbers 2-3, August 2005.
> 
> 2. M. Gelfond and V. Lifschitz. Classical negation in logic programs and
> deductive databases. New Generation Computing, 9:365--385, 1991.
> 


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Hassan Aït-Kaci
ILOG, Inc. - Product Division R&D
tel/fax: +1 (604) 930-5603 - email: hak @ ilog . com

Received on Thursday, 8 June 2006 16:04:19 UTC