Interpolation in Equilibrium Logic and Answer Set Programming: the Propositional Case

TL;DR

This paper investigates the interpolation property in propositional equilibrium logic and answer set programming, establishing various forms of interpolation and their implications for logic programs and variable forgetting.

Contribution

It provides the first detailed analysis of interpolation in propositional equilibrium logic and its applications to answer set programming and variable forgetting.

Findings

Established weaker and stronger forms of interpolation depending on inference interpretation.

Derived interpolation results for ground logic programs under answer set semantics.

Explored uniform interpolation and variable forgetting in disjunctive logic programs.

Abstract

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the non-monotonic system of equilibrium logic, establishing weaker or stronger forms of interpolation depending on the precise interpretation of the inference relation. These results also yield a form of interpolation for ground logic programs under the answer sets semantics. For disjunctive logic programs we also study the property of uniform interpolation that is closely related to the concept of variable forgetting.