{"type":"ScholarlyArticle","title":"Solving the Satisfiability Problem of Modal Logic S5 Guided by Graph Coloring","authors":[{"name":"Pei Huang","slug":"pei-huang","given":"Pei","family":"Huang","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"},{"name":"Minghao Liu","slug":"minghao-liu","given":"Minghao","family":"Liu","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"},{"name":"Ping Wang","slug":"ping-wang","given":"Ping","family":"Wang","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"},{"name":"Wenhui Zhang","slug":"wenhui-zhang","given":"Wenhui","family":"Zhang","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"},{"name":"Feifei Ma","slug":"feifei-ma","given":"Feifei","family":"Ma","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; Laboratory of Parallel Software and Computational Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"},{"name":"Jian Zhang","slug":"jian-zhang","given":"Jian","family":"Zhang","affiliation":"State Key Laboratory of Computer Science , ISCAS , China; University of Chinese Academy of Sciences {huangpei ,"}],"abstract":"Modal logic S5 has found various applications in artificial intelligence. With the advances in modern SAT solvers, SAT-based approach has shown great potential in solving the satisfiability problem of S5. The scale of the SAT encoding for S5 is strongly influenced by the upper bound on the number of possible worlds. In this paper, we present a novel SAT-based approach for S5 satisfiability problem. We show a normal form for S5 formulas. Based on this normal form, a conflict graph can be derived whose chromatic number provides an upper bound of the possible worlds and a lot of unnecessary search spaces can be eliminated in this process. A heuristic graph coloring algorithm is adopted to balance the efficiency and optimality. The number of possible worlds can be significantly reduced for many practical instances. Extensive experiments demonstrate that our approach outperforms state-of-the-art S5-SAT solvers.","doi":"10.24963/ijcai.2019/153","url":"https://ijcai.org/proceedings/2019/153","pdf":"https://ijcai.org/proceedings/2019/0153.pdf","markdown":"https://ijcai.org/proceedings/2019/153.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/153","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Constraints and SAT","track":"Main track","number":153,"pages":{"first":1093,"last":1100},"keywords":["Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving","Constraints and SAT: Constraint Satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Abate et al., 2007] Pietro Abate, Rajeev Goré, and Florian Widmann. 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