Combining explicit negation and negation by failure via Belnap's logic

AbstractThis paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two different forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and an answer sets' semantics that is shown to be equivalent to that of Gelfond and Lifschitz.The proofs rely on a translation into normal programs, and on a variant of Fitting's extension of logic programming to bilattices

Negation-as-failure considered harmful

In logic programs, negation-as-failure has been used both for representing negative information and for providing default nonmonotonic inference. In this paper we argue that this twofold role is not only unnecessary for the expressiveness of the language, but it also plays against declarative programming, especially if further negation symbols such as strong negation are also available. We therefore propose a new logic programming approach in which negation and default inference are independent, orthogonal concepts. Semantical characterization of this approach is given in the style of answer sets, but other approaches are also possible. Finally, we compare them with the semantics for logic programs with two kinds of negation.Red de Universidades con Carreras en Informática (RedUNCI