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A PURELY SYNTACTIC AND CUT-FREE SEQUENT CALCULUS FOR THE MODAL LOGIC OF PROVABILITY

  • FRANCESCA POGGIOLESI (a1)
Abstract

In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. No explicit semantic element is used in the sequent calculus and all the results are proved in a purely syntactic way.

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*CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE, VRIJE UNIVERSITEIT BRUSSEL, ETTERBEEK CAMPUS, PLEINLAAN 2, B-1050 BRUSSELS, BELGIUM E-mail:poggiolesi@gmail.com
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R Kashima . (1994). Cut-free sequent calculi for some tense logics. Studia Logica, 53, 119135.

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

S Valentini . (1983). The modal logic of provability: Cut-elimination. Journal of Philosophical Logic, 12, 471476.

H Wansing . (1994). Sequent calculi for normal modal propositional logics. Journal of Logic and Computation, 4, 125142.

H Wansing . (2002). Sequent systems for modal logics. In D. Gabbay and F. Guenther , editors. Handbook of Philosophical Logic (second edition). Dordrecht: Kluwer, pp. 61145.

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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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