Towards a first order equilibrium logic for nonmonotonic reasoning

Abstract

Equilibrium logic, introduced in [20], is a conservative extension of answer set semantics for logic programs to the full language of propositional logic. In this paper we initiate the study of first-order variants of equilibrium logic. In particular, we focus on a quantified version QN5 of the propositional many-valued logic N5 of here-and-there with strong negation, and define the condition of equilibrium via a minimal model construction. We verify Skolem forms and Herbrand theorems for QN5 and show that, like its propositional counterpart, the quantified version of equilibrium logic also conservatively extends answer set semantics.