about "strong" negation

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.

-- 
Dr. Axel Polleres
email: axel@polleres.net  url: http://www.polleres.net/

Received on Thursday, 8 June 2006 15:50:58 UTC