A logic program Π 1 is said to be equivalent to a logic program Π 2 in the sense of the answer set semantics if Π 1 and Π 2 have the same answer sets. We are interested in the following stronger condition: for every logic program, Π, Π 1 , ∪ Π has the same answer sets as Π 2 ∪ Π. The study of strong equivalence is important, because we learn from it how one can simplify a part of a logic program without looking at the rest of it. The main theorem shows that the verification of strong equivalence can be accomplished by cheching the equivalence of formulas in a monotonic logic, called the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic.

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Equilibrium logic is a general purpose nonmonotonic reasoning formalism closely aligned with answer set programming (ASP). In particular it provides a logical foundation for ASP as well as an extension of the basic syntax of answer set programs. We present an overview of equilibrium logic and its main properties and uses.

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