A Tableau Calculus for MaxSAT Based on Resolution

Abstract

We define a new MaxSAT tableau calculus based on resolution. Given a multiset of propositional clauses ϕ, we prove that the calculus is sound in the sense that if the minimum number of contradictions derived among the branches of a completed tableau for ϕ is m, then the minimum number of unsatisfied clauses in ϕ is m. We also prove that it is complete in the sense that if the minimum number of unsatisfied clauses in ϕ is m, then the minimum number of contradictions among the branches of any completed tableau for ϕ is m. Moreover, we describe how to extend the proposed calculus to solve Weighted Partial MaxSAT.