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PROOF SYSTEMS FOR VARIOUS FDE-BASED MODAL LOGICS

  • SERGEY DROBYSHEVICH (a1) and HEINRICH WANSING (a2)

Abstract

We present novel proof systems for various FDE-based modal logics. Among the systems considered are a number of Belnapian modal logics introduced in Odintsov & Wansing (2010) and Odintsov & Wansing (2017), as well as the modal logic KN4 with strong implication introduced in Goble (2006). In particular, we provide a Hilbert-style axiom system for the logic $BK^{\square - } $ and characterize the logic BK as an axiomatic extension of the system $BK^{FS} $ . For KN4 we provide both an FDE-style axiom system and a decidable sequent calculus for which a contraction elimination and a cut elimination result are shown.

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*LABORATORY OF COMPUTABILITY THEORY AND APPLIED LOGIC SOBOLEV INSTITUTE OF MATHEMATICS NOVOSIBIRSK, 630090, RUSSIAN FEDERATION E-mail: drobs@math.nsc.ru
INSTITUTE OF PHILOSOPHY I RUHR UNIVERSITY BOCHUM BOCHUM, 44801, GERMANY E-mail: Heinrich.Wansing@ruhr-uni-bochum.de

References

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