Solving Problems in the Polynomial Hierarchy with ASP(Q)

Giovanni Amendola, Bernardo Cuteri, Francesco Ricca, Mirek Truszczynski

Abstract: Answer Set Programming with Quantifiers ASP(Q) is a recent extension of Answer Set Programming (ASP) that allows one to model problems from the entire polynomial hierarchy. Earlier work focused on demonstrating modeling capabilities of ASP(Q). In this paper, we propose a modular ASP(Q) solver that translates a quantified ASP program together with a given data instance into a Quantified Boolean Formula (QBF) to be solved by any QBF solver. We evaluate the performance of our solver on several instances and with different back-end QBF solvers, demonstrating the efficacy of ASP(Q) as a tool for rapid modeling and solving of complex combinatorial problems. The benchmark problems we use include two new ones, Argumentation Coherence and Para-coherent ASP, for which we develop elegant ASP(Q) encodings.