A General Theorem Prover for Quantified Modal Logics
The main contribution of this work is twofold. It presents a modular tableau calculus, in the free-variable style, treating the main domain variants of quantified modal logic and dealing with languages where rigid and non-rigid designation can coexist. The calculus uses, to this end, light and simple semantical annotations. Such a general proof-system results from the fusion into a unified framework of two calculi previously defined by the second and third authors. Moreover, the work presents a theorem prover, called GQML-Prover, based on such a calculus, which is accessible in the Internet. The fair deterministic proof-search strategy used by the prover is described and illustrated via a meaningful example.
KeywordsModal Logic Intuitionistic Logic Variable Assignment Ground Term Dynamic Rule
Unable to display preview. Download preview PDF.
- 1.B. Beckert and R. Goré. Free variable tableaux for propositional modal logics. In Proc. of TABLEAUX’97, pages 91–106. Springer, 1997.Google Scholar
- 2.S. Cerrito and M. Cialdea Mayer. Free-variable tableaux for constant-domain quantified modal logic with rigid and non-rigid designation. In First Int. Joint Conf. on Automated Reasoning (IJCAR 2001), pages 137–151. Springer, 2001.Google Scholar
- 3.M. Cialdea Mayer and S. Cerrito. Variants of first-order modal logics. In Proc. of TABLEAUX 2000, pages 175–189. Springer, 2000.Google Scholar
- 6.M. Fitting. Proof Methods for Modal and Intuitionistic Logics. Reidel, 1983.Google Scholar
- 7.M. Fitting. First-Order Logic and Automated Theorem Proving. Springer, 1996.Google Scholar
- 8.M. Fitting and R Mendelsohn. First-Order Modal Logic. Kluwer, 1998.Google Scholar
- 9.R. Goré. Automated reasoning project. Technical report, TR-ARP-15-95, 1997.Google Scholar
- 11.U. Hustadt and R. A. Schmidt. Simplification and backjumping in modal tableau. In Proc. of TABLEAUX’98, pages 187–201. Springer, 1998.Google Scholar
- 12.Jens Otten. ileanTAP: An intuitionistic theorem prover. In Proc. of TABLEAUX’97, pages 307–312. Springer, 1997.Google Scholar
- 13.J. Posegga and P. Schmitt. Implementing semantic tableaux. In M. D’Agostino, G. Gabbay, R. Hähnle, and J. Posegga, editors, Handbook of tableau method, pages 581–629. Kluwer, 1999.Google Scholar
- 14.V. Thion. A strategy for free variable tableaux for variant of quantified modal logics. Technical report, L.R.I., 2002. http://www.lri.fr/~thion.
- 15.L. A. Wallen. Automated Deduction in Nonclassical Logics: Efficient Matrix Proof Methods for Modal and Intuitionistic Logics. MIT Press, 1990.Google Scholar