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PROOF SYSTEMS FOR VARIOUS FDE-BASED MODAL LOGICS

Published online by Cambridge University Press:  17 June 2019

SERGEY DROBYSHEVICH  and
HEINRICH WANSING
SERGEY DROBYSHEVICH*
Affiliation:
Laboratory of Computability Theory and Applied Logic, Sobolev Institute of Mathematics
HEINRICH WANSING*
Affiliation:
Institute of Philosophy I, Ruhr University Bochum
*
*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
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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.

Keywords

03B4503F52sequent calculimodal logicfirst degree entailmentcut-eliminationstrong implication

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 720 - 747
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Copyright
Copyright © Association for Symbolic Logic 2019 

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