Interpolable Formulas in Equilibrium Logic and Answer Set Programming

Dov Gabbay, David Pearce, Agustin Valverde

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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 the non-monotonic system of e quilibrium 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. The first-order version of equilibrium logic has analogous Interpolation properties whenever the collection of equilibrium models is (first-order) definable. Since this is the case for so-called safe programs and theories, it applies to the usual situations that arise in practical answer set programming.
Original languageEnglish
Pages (from-to)917 - 943
Number of pages27
JournalJournal Artificial Intelligence Research
Volume42
Publication statusPublished - Sept 2011

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