On The Propositional SLDNF-Resolution

We consider propositional logic programs with negations. We define notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued fix-point or declarative semantics for program P are equivalent to the two-valued semantics for the constructive version of P . We argue that it would be beneficial to replace Negation as Failure by constructive transformation, and it would be beneficial to use the two-valued semantics for the constructive version of the program instead of multivalued semantics for the original program. Keywords: Logic programming, declarative programming, negation as failure, nonclassical logics, three-valued semantics. 1. Introduction This paper is concerned with declarative interpretations of logic programs using several logical syst..