  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 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. 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.
