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PROOF SYSTEMS FOR VARIOUS FDE-BASED MODAL LOGICS
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- Journal:
- The Review of Symbolic Logic / Volume 13 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 17 June 2019, pp. 720-747
- Print publication:
- December 2020
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- Article
- Export citation
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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.
