On the Propositional SLDNF-Resolution

We consider propositional logic programs with negations. We deene 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 x-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 beneecial to replace Negation as Failure by constructive transformation , and it would be beneecial to use the two-valued semantics for the constructive version of the program instead of multivalued semantics for the original program.