A resolution calculus for MinSAT-Reference-Cited by-同舟云学术

A resolution calculus for MinSAT

Published:2019-10-23 Issue:1 Volume:29 Page:28-44
ISSN:1367-0751
Container-title:Logic Journal of the IGPL
language:en
Short-container-title:

Author:

Li Chu-Min¹,Xiao Fan²,Manyà Felip³

Affiliation:

1. School of Computer Science, Huazhong University of Science and Technology, 430074 Wuhan, China and MIS, Université de Picardie Jules Verne, 80080 Amiens, France

2. School of Computer Science, Huazhong University of Science and Technology, 430074 Wuhan, China

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

Abstract

Abstract The logical calculus for SAT are not valid for MaxSAT and MinSAT because they preserve satisfiability but not the number of unsatisfied clauses. To overcome this drawback, a MaxSAT resolution rule preserving the number of unsatisfied clauses was defined in the literature. This rule is complete for MaxSAT when it is applied following a certain strategy. In this paper we first prove that the MaxSAT resolution rule also provides a complete calculus for MinSAT if it is applied following the strategy proposed here. We then describe an exact variable elimination algorithm for MinSAT based on that rule. Finally, we show how the results for Boolean MinSAT can be extended to solve the MinSAT problem of the multiple-valued clausal forms known as signed conjunctive normal form formulas.

Funder

EU H2020 Research and Innovation Programme

Ministerio de Economía y Competitividad

Publisher

Oxford University Press (OUP)

Subject

Logic

Link

http://academic.oup.com/jigpal/article-pdf/29/1/28/35933772/jzz028.pdf

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