Logic and Logical Philosophy 20 (3):189-203 (2011)

Andrzej Indrzejczak
University of Lodz
We present a detailed proof of the admissibility of cut in sequent calculus for some congruent modal logics. The result was announced much earlier during the Trends in Logic Conference, Toruń 2006 and the proof for monotonic modal logics was provided already in Indrzejczak [5]. Also some tableau and natural deduction formalizations presented in Indrzejczak [6] and Indrzejczak [7] were based on this result but the proof itself was not published so far. In this paper we are going to fill this gap. The delay was partly due to the fact that the author from time to time was trying to improve the result and extend it to some additional logics by testing other methods of proving cut elimination. Unfortunately all these attempts failed and cut elimination holds only for these logics which were proved to satisfy this property already in 2005.
Keywords cut elimination  modal logics  proof methods  sequent calculi
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DOI 10.12775/LLP.2011.010
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References found in this work BETA

[Omnibus Review].R. A. Bull - 1985 - Journal of Symbolic Logic 50 (1):231-234.
Sequent Calculi for Monotonic Modal Logics.Andrzej Indrzejczak - 2005 - Bulletin of the Section of Logic 34 (3):151-164.
Labelled Tableau Calculi for Weak Modal Logics.Andrzej Indrzejczak - 2007 - Bulletin of the Section of Logic 36 (3-4):159-173.

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