A Tableau Calculus for Non-clausal Maximum Satisfiability

We define a non-clausal MaxSAT tableau calculus. Given a multiset of propositional formulas F, 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 F is m, then the minimum number of unsatisfied formulas in F is m. We also prove that it is complete in the sense that if the minimum number of unsatisfied formulas in F is m, then the minimum number of contradictions among the branches of any completed tableau for F is m. Moreover, we describe how to extend the proposed calculus to deal with hard and weighted soft formulas