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We introduce the notion of X-stable models parametrized by a given logic X. Such notion is based on a construction that we call weak completions: a set of atoms M is an X-stable model of a theory T if M is a model of T, in the sense of classical logic, and the weak completion of T (namely T [ : e M) can prove, in the sense given by logic X, every atom in… (More)

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intu-itionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove… (More)

We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more general point of view. Our definition, based on intuitionistic logic and following ideas from D. Pearce [Stable inference as intuitionistic validity, Logic Programming 38 (1999) 79–91],… (More)

We study logic programs under Gelfond's translation in the context of modal logic S5. We show that for arbitrary logic programs (propositional theories where logic negation is associated with default negation) ground nonmonotonic modal logics between T and S5 are equivalent. Furthermore, we also show that these logics are equivalent to a nonmonotonic logic… (More)

A-Prolog, Answer Set Programming or Stable Model Programming, is an important outcome of the theoretical work on Nonmonotonic Reasoning and AI applications of Logic Programming in the last 15 years. In the full version of this paper we study interesting applications of logic in the field of answer sets. Two popular software implementations to compute answer… (More)

We study the notion of strong equivalence between two dis-junctive logic programs under the G 3-stable model semantics, also called the P-stable semantics, and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in some paraconsistent logics or in some cases in classical logic.… (More)