Abstract
The goal of this paper is to propose a new technique for developing decision procedures for propositional modal logics. The basic idea is that propositional modal decision procedures should be developed on top of propositional decision procedures. As a case study, we describe an algorithm, based on an implementation of the Davis-Putnam-Longemann-Loveland procedure, which tests satisfiability in modal K. The algorithm is compared with a tableau based decision procedure. The experimental results show that our algorithm outperforms this system. The testing is performed following a newly developed methodology which, among other things, allows us to classify problems according to an easy to hard pattern.
This work has benefited from many long discussions with Enrico Giunchiglia. Enrico played a crucial role in the development of Version 1 of the algorithm described in this paper. Bernhard Nebel and Enrico Franconi have given us access to the tableau implementation used in the tests described in this paper. Marco Roveri has given technical assistance in the testing phase. All the members of the Mechanized Reasoning Group in Genoa are thanked for putting up with many weeks of CPU-time background processes.
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References
A. Armando and E. Giunchiglia. Embedding Complex Decision Procedures inside an Interactive Theorem Prover. Annals of Mathematics and Artificial Intelligence, 8(3–4):475–502, 1993.
M. Buro and H. Buning. Report on a SAT competition. Technical Report 110, University of Paderborn, Germany, November 1992.
R. E. Bryant. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys, 24(3):293–318, September 1992.
M. D'Agostino. Are Tableaux an Improvement on Truth-Tables? Journal of Logic, Language and Information, 1:235–252, 1992.
M. Davis, G. Longemann, and D. Loveland. A machine program for theorem proving. Journal of the ACM, 5(7), 1962.
M. D'Agostino and M. Mondadori. The Taming of the Cut. Journal of Logic and Computation, 4(3):285–319, 1994.
M. Fitting. First-Order Modal Tableaux. Journal of Automated Reasoning, 4:191–213, 1988.
M. L. Ginsberg. Dynamic Backtracking. Journal of Artificial Intelligence Research, 1:25–46, 1993.
F. Giunchiglia and L. Serafini. Multilanguage hierarchical logics (or: how we can do without modal logics). Artificial Intelligence, 65:29–70, 1994.
F. Giunchiglia, L. Serafini, E. Giunchiglia, and M. Frixione. NonOmniscient Belief as Context-Based Reasoning. In Proc. IJCAI13, pages 548–554, 1993.
J.Y. Halpern and Y. Moses. A guide to the completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54(3):319–379, 1992.
B. Hollunder, W. Nutt, and M. Schmidt-Schauß. Subsumption Algorithms for Concept Description Languages. In Proc. ECAI8, pages 348–353, 1990.
F. Massacci. Strongly analytic tableaux for normal modal logics. In Proc. CADE12, 1994.
D. Mitchell, B. Selman, and H. Levesque. Hard and Easy Distributions of SAT Problems. In Proc. AAAI10, pages 459–465, 1992.
K. D. Schild. A correspondence theory for terminological logics: preliminary report. In Proc. IJCAI12, pages 466–471, 1991.
R. Sebastiani. Applying GSAT to Non-Clausal Formulas. Journal of Artificial Intelligence Research, 1:309–314, 1994.
B. Selman, H. Levesque., and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Proc. AAAI10, pages 440–446, 1992.
C. B. Suttner and G. Sutcliffe. The TPTP Problem Library. Technical Report TR 95/6, James Cook University, Australia, August 1995.
M. Schmidt-Schauß and G. Smolka. Attributive Concept Descriptions with Complements. Artificial Intelligence, 48:1–26, 1991.
T. E. Uribe and M. E. Stickel. Ordered Binary Decision Diagrams and the Davis-Putnam Procedure. In Proc. of the 1st International Conference on Constraints in Computational Logics, 1994.
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© 1996 Springer-Verlag Berlin Heidelberg
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Giunchiglia, F., Sebastiani, R. (1996). Building decision procedures for modal logics from propositional decision procedures — The case study of modal K. In: McRobbie, M.A., Slaney, J.K. (eds) Automated Deduction — Cade-13. CADE 1996. Lecture Notes in Computer Science, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61511-3_115
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DOI: https://doi.org/10.1007/3-540-61511-3_115
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