The valid model semantics for logic programs

TL;DR: The valid model semantics is a three-valued semantics, and is defined in terms of a ‘normal form’ computation, which extends the well-founded semantics in a natural manner, and has several advantages over it.

Abstract: We present the valid model semantics, a new approach to providing semantics for logic programs with negation, set-terms and grouping. The valid model semantics is a three-valued semantics, and is defined in terms of a ‘normal form’ computation. The valid model semantics also gives meaning to the generation and use of non-ground facts (i.e., facts with variables) in a computation.The formulation of the semantics in terms of a normal form computation offers important insight not only into the valid model semantics, but also into other semantics proposed earlier. We show that the valid model semantics extends the well-founded semantics in a natural manner, and has several advantages over it. The well-founded semantics can also be undertood using a variant of the normal form computations that we use; the normal form computations used for valid semantics seem more natural than those used for well-founded semantics.We also show that the valid model semantics has several other desirable properties: it is founded ([SZ90]), it is contained in every regular model ([YY90]), and it is contained in every two-valued stable model.