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A CUT-FREE SIMPLE SEQUENT CALCULUS FOR MODAL LOGIC S5

  • FRANCESCA POGGIOLESI (a1)
Abstract

In this paper, we present a simple sequent calculus for the modal propositional logic S5. We prove that this sequent calculus is theoremwise equivalent to the Hilbert-style system S5, that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way.

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*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF FLORENCE, 50139 FLORENCE, ITALY. E-mail: francesca.poggiolesi@unifi.it
References
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Avron A. (1996). The method of hypersequents in the proof theory of propositional non-classical logic. In Hodges W., Hyland M., Steinhorn C., & Truss J., editors. Logic: From Foundations to Applications. Oxford University Press, pp. 132.
Blumey S., & Humberstone L. (1991). A perspective on modal sequent logic. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 27, 763782.
Braüner T. (2000). A cut-free Gentzen formulation of the modal logic S5. Logic Journal of the IGPL, 8, 629643.
Brünnler K. (2006). Deep sequent systems for modal logic. Advances in Modal Logic AiML, 6, 107119.
Cerrato C. (1993). Cut-free modal sequents for normal modal logics. Notre-Dame Journal of Formal Logic, 34, 564582.
Došen K. (1985). Sequent systems for modal logic. Journal of Symbolic Logic, 50, 149159.
Indrezejczak A. (1997). Generalised sequent calculus for propositional modal logics. Logica Trianguli, 1, 1531.
Matsumoto K., & Ohnishi M. (1959). Gentzen method in modal calculi. Osaka Mathematical Journal, 11, 115120.
Mints G. (1997). Indexed systems of sequents and cut-elimination. Journal of Philosophical Logic, 26, 671696.
Negri S. (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34, 507534.
Poggiolesi F. (2006). Sequent calculus for modal logic. Logic Colloquium.
Poggiolesi F. (2007, submitted). Two cut-free sequent calculi for modal logic S5. Proceedings of SILFS Conference.
Poggiolesi F. (2008). Sequent calculi for modal logic. Ph.D Thesis, p. 1224, Florence.
Poggiolesi F. (2008, to appear). The method of tree-hypersequent for modal propositional logic. Trends in Logic IV, Studia Logica Library.
Restall G. (2006, to appear). Sequents and circuits for modal logic. Proceedings of Logic Colloquium.
Sato M. (1980). A cut-free Gentzen-type system for the modal logic s5. Journal of Symbolic Logic, 45, 6784.
Wansing H. (1994). Sequent calculi for normal modal propositional logics. Journal of Logic and Computation, 4, 125142.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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