First-order Answer Set Programming As Constructive Proof Search

We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Sigma_1 level of the Mints hierarchy in first-order intuitionistic logic. It follows that Sigma_1 formulas using predicates of fixed arity (in particular unary) is of the same strength as FOASP. Our construction reveals a close similarity between constructive provability and stable entailment, or equivalently, between the construction of an answer set and an intuitionistic refutation. This paper is under consideration for publication in Theory and Practice of Logic Programming