The MaxSAT Problem in the Real-Valued MV-Algebra

Abstract

AbstractThis work addresses the maximum satisfiability (MaxSAT) problem for a multiset of arbitrary formulas of the language of propositional Łukasiewicz logic over the MV-algebra whose universe is the real interval [0,1]. First, we reduce the MaxSAT problem to the SAT problem over the same algebra. This solution method sets a benchmark for other approaches, allowing a classification of the MaxSAT problem in terms of metric reductions introduced by Krentel. We later define an alternative analytic method with preprocessing in terms of a Tseitin transformation of the input, followed by a reduction to a system of linear constraints, in analogy to the earlier approaches of Hähnle and Olivetti. We discuss various aspects of these approaches to solving the problem.