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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
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S. Blumey , & L Humberstone . (1991). A perspective on modal sequent logic. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 27, 763782.

T Braüner . (2000). A cut-free Gentzen formulation of the modal logic S5. Logic Journal of the IGPL, 8, 629643.

C Cerrato . (1993). Cut-free modal sequents for normal modal logics. Notre-Dame Journal of Formal Logic, 34, 564582.

K Došen . (1985). Sequent systems for modal logic. Journal of Symbolic Logic, 50, 149159.

G Mints . (1997). Indexed systems of sequents and cut-elimination. Journal of Philosophical Logic, 26, 671696.

S Negri . (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34, 507534.

M Sato . (1980). A cut-free Gentzen-type system for the modal logic s5. Journal of Symbolic Logic, 45, 6784.

H Wansing . (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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