Computing Stable Models via Reductions to Difference Logic

Abstract

Propositional satisfiability (SAT) solvers provide a promising computational platform for logic programs under the stable model semantics. However, computing stable models of a logic program using a SAT solver presumes translating the program into a set of clauses which is the input form accepted by most SAT solvers. This leads to fairly complex super-linear translations. There are, however, interesting extensions to plain clausal propositional representations such as difference logic. A number of solvers have been developed for difference logic, in particular in the context of the satisfiability modulo theories (SMT) framework, and the goal of the paper is to study whether such engines could be harnessed to the computation of stable models for logic programs in an effective way. To this end, we provide succinct translations from logic programs to theories of difference logic and evaluate the potential of SMT solvers in the computation of stable models using these translations and a selection of benchmarks.