Applications of Intuitionistic Logic in Answer Set Programming

TL;DR

This paper explores the use of intermediate logics, especially intuitionistic logic, to analyze and characterize answer set semantics in logic programming, establishing new links and properties relevant to ASP.

Contribution

It introduces novel characterizations of answer sets using intuitionistic provability and logic G3, connecting ASP semantics with intermediate logics and extending existing results.

Findings

Characterization of answer sets via intuitionistic provability.

Identification of logic G3 as characterizing strong equivalence.

Insights into minimal models within answer set semantics.

Abstract

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.