Compact Translations of Non-disjunctive Answer Set Programs to Propositional Clauses

Abstract

Propositional satisfiability (SAT) solvers provide a promising computational platform for logic programs under the stable model semantics. Computing stable models of a logic program using a SAT solver presumes translating the program into a set of clauses in the DIMACS format which is accepted by most SAT solvers as input. In this paper, we present succinct translations from programs with choice rules, cardinality rules, and weight rules—also known as smodels programs—to sets of clauses. These translations enable us to harness SAT solvers as black boxes to the task of computing stable models for logic programs generated by any smodels compatible grounder such as lparse or gringo. In the experimental part of this paper, we evaluate the potential of SAT solver technology in finding stable models using NP-complete benchmark problems employed in the Second Answer Set Programming Competition.