Clause tableaux for maximum and minimum satisfiability

Author:

Argelich Josep1,Li Chu Min2,Manyà Felip3,Soler Joan Ramon3

Affiliation:

1. Departament d' Informàtica i Enginyeria Industrial (DIEI), Universitat de Lleida, 25001 Lleida, Spain

2. MIS, Université de Picardie Jules Verne, 80039 Amiens, France

3. Artificial Intelligence Research Institute (IIIA, CSIC), 08193 Bellaterra, Spain

Abstract

Abstract The inference systems proposed for solving SAT are unsound for solving MaxSAT and MinSAT, because they preserve satisfiability but not the minimum and maximum number of clauses that can be falsified, respectively. To address this problem, we first define a clause tableau calculus for MaxSAT and prove its soundness and completeness. We then define a clause tableau calculus for MinSAT and also prove its soundness and completeness. Finally, we define a complete clause tableau calculus for solving both MaxSAT and MinSAT, in that the minimum number of generated empty clauses provides an optimal MaxSAT solution and the maximum number provides an optimal MinSAT solution.

Funder

Project LOGISTAR

EU H2020 Research and Innovation Programme under

MINECO-FEDER projects RASO

Publisher

Oxford University Press (OUP)

Subject

Logic

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