Cut-Free Tableau Calculi for some Intuitionistic Modal Logics
- Mauro Ferrari
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In this paper we provide cut-free tableau calculi for the intuitionistic modal logics IK, ID, IT, i.e. the intuitionistic analogues of the classical modal systems K, D and T. Further, we analyse the necessity of duplicating formulas to which rules are applied. In order to develop these calculi we extend to the modal case some ideas presented by Miglioli, Moscato and Ornaghi for intuitionistic logic. Specifically, we enlarge the language with the new signs Fc and CR near to the usual signs T and F. In this work we establish the soundness and completeness theorems for these calculi with respect to the Kripke semantics proposed by Fischer Servi.
- Amati, G., Pirri, F. (1994) A uniform tableau method for intuitionistic modal logics I*. Studia Logica 53: pp. 29-60
- M.J. Cresswell and G.E. Hughes, 1984, A Companion to Modal Logic, Methuen.
- Fischer Servi, G. (1981) Completeness for non normal intuitionistic modal logics. Note di Matematica 1: pp. 203-212
- Fischer Servi, G. (1984) Axiomatizations for some intuitionistic modal logics. Rend. Sem. Mat. Univers. Polit. Torino 42: pp. 179-194
- Fitting, M. (1983) Proof Methods for Modal and Intuitionistic Logics. Reidel, Dordrecht
- Gabbay, D.M. (1981) Semantical Investigations in Heyting's Intuitionistic Logic. Reidel, Dordrecht
- P. Miglioli, U. Moscato, and M. Ornaghi, 1994, How to avoid duplications in refutation systems for intuitionistic logic and Kuroda logic, In K. Broda, M. D'Agostino, R. Goré, R. Johnson, and S. Reeves, editors, Theorem Proving with Analytic Tableaux and Related Methods: 3rd International Workshop, Abingdon, U.K., 169–187.
- Miglioli, P., Moscato, U., Ornaghi, M. (1994) An improved refutation system for intuitionistic predicate logic. Journal of Automated Reasoning 12: pp. 361-373
- P. Miglioli, U. Moscato, and M. Ornaghi, 1995, Refutation systems for propositional modal logics, In P. Baumgartner, R. Hänle, and J. Posegga, editors, Theorem Proving with Analytic Tableaux and Related Methods: 4th International Workshop, Schloss Rheinfels, St. Goar, Germany, volume 918, 95–105. Springer-Verlag.
- G. Plotkin and C. Stirling, 1986, A framework for intuitionistic modal logic, In J.Y. Halpern, editor, Theoretical Aspects of Reasoning about Knowledge, 399–406, Morgan-Kaufmann.
- Smullyan, R.M. (1968) First-Order Logic. Springer, Berlin
- Cut-Free Tableau Calculi for some Intuitionistic Modal Logics
Volume 59, Issue 3 , pp 303-330
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- Online ISSN
- Kluwer Academic Publishers
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- intuitionistic modal logics
- refutation systems
- Kripke models
- Mauro Ferrari (1)
- Author Affiliations
- 1. Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135, Milano, Italy