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.