论文信息 - Computing with Cylindric Modal Logics and Arrow Logics, Lower Bounds

Computing with Cylindric Modal Logics and Arrow Logics, Lower Bounds

The complexity of the satisfiability problems of various arrow logics and cylindric modal logics is determined. As is well known, relativising these logics makes them decidable. There are several parameters that can be set in such a relativisation. We focus on the following three: the number of variables involved, the similarity type and the kind of relativised models considered. The complexity analysis shows the importance and relevance of these parameters.

Maarten Marx

[1] Richard E. Ladner,et al. The Computational Complexity of Provability in Systems of Modal Propositional Logic , 1977, SIAM J. Comput..

[2] Moshe Y. Vardi. Why is Modal Logic So Robustly Decidable? , 1996, Descriptive Complexity and Finite Models.

[3] A. Tarski,et al. A Formalization Of Set Theory Without Variables , 1987 .

[4] Maarten Marx,et al. Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables , 1999, J. Symb. Log..

[5] J.F.A.K. van Benthem,et al. Modal logic and classical logic , 1983 .

[6] Johan van Benthem,et al. Exploring logical dynamics , 1996, Studies in logic, language and information.

[7] Joseph Y. Halpern,et al. A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief , 1992, Artif. Intell..

[8] Maarten Marx,et al. Undecidable Relativizations of Algebras of Relations , 1999, J. Symb. Log..

[9] Richard E. Ladner,et al. Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[10] Ian M. Hodkinson,et al. Finite algebras of relations are representable on finite sets , 1999, Journal of Symbolic Logic.

[11] Yde Venema,et al. Many-dimensional Modal Logic , 1991 .

[12] Erich Grädel,et al. On the Restraining Power of Guards , 1999, Journal of Symbolic Logic.

[13] István Németi. A fine-structure analysis of first-order logic , 1997 .