SLX - A Top-down Derivation Procedure for Programs with Explicit Negation

In this paper we deene a sound and (theoretically) complete top-down derivation procedure for a well-founded semantics of logic programs extended with explicit negation (WFSX). By its nature, it is amenable to a simple interpreter implementation in Prolog, and readily allows pre-processing into Prolog, showing promise as an eecient basis for further development. The derivation method is directly inspired on the semantic AND-tree characterization of WFSX in our paper 2], but does not require knowledge of it. In fact, that work can be seen as a preliminary step towards the deenition of the procedure presented here. Because of its properties, which are paramount for top-down query evaluation and other approaches do not fully enjoy, WFSX is a natural candidate to being the semantics of choice for logic programs extended with explicit negation. Moreover, WFSX is sound wrt to the answer-sets semantics, and it is a better aproximation to answer-sets than simply using the well-founded semantics of normal programs, plus a renaming of explicitly negated literals. Thus, our top-down procedure can be used as a sound one for answer-sets, that provides less incompleteness than others. Since WFSX coincides with the well-founded semantics on normal programs, our method is applicable to it and, for ground programs, compares favourably with previous approaches 2].