Applications of Intuitionistic Logic in Answer Set Programming

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, intuitionistic 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 properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Computing Preferred Safe Beliefs

We recently proposed a definition of a language for nonmonotonic reasoning based on intuitionistic logic. Our main idea is a generalization of the notion of answer sets for arbitrary propositional theories. We call this extended framework safe beliefs. We present an algorithm, based on the Davis-Putnam (DP) method, to compute safe beliefs for arbitrary propositional theories. We briefly discuss some ideas on how to extend this paradigm to incorporate preferences