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Interpolation is an important property of classical and many non-classicallogics that has been shown to have interesting applications in computer scienceand AI. Here we study the Interpolation Property for the the non-monotonicsystem of equilibrium logic, establishing weaker or stronger forms ofinterpolation depending on the precise interpretation of the inferencerelation. These results also yield a form of interpolation for ground logicprograms under the answer sets semantics. For disjunctive logic programs wealso study the property of uniform interpolation that is closely related to theconcept of variable forgetting. The first-order version of equilibrium logichas analogous Interpolation properties whenever the collection of equilibriummodels is (first-order) definable. Since this is the case for so-called safeprograms and theories, it applies to the usual situations that arise inpractical answer set programming.

Interpolable Formulas in Equilibrium Logic and Answer Set Programming