5 research outputs found
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
Answer Set Programming and S4
We develop some ideas in order to obtain a nonmonotonic reasoning system based on the modal logic S4. As a consequence we show how to express the well known answer set semantics using a restricted fragment of modal formulas. Moreover, by considering the full set of modal formulas, we obtain an interesting generalization of answer sets for logic programs with modal connectives. We also depict, by the use of examples, possible applications of this inference system.
It is also possible to replace the modal logic S4 with any other modal logic to obtain similar nonmonotonic systems. We even consider the use of multimodal logics in order to model the knowledge and beliefs of agents in a scenario where their ability to reason about each other’s knowledge is relevant. Our results clearly state interesting links between answer sets, modal logics and multi-agent systems