Studia Logica 105 (1):93-119 (2017)

Authors
Andreas Fjellstad
University of Bergen
Abstract
In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between derivable sequents and validity in comparison to the calculus developed by Ripley.
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DOI 10.1007/s11225-016-9683-y
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
Structural Reflexivity and the Paradoxes of Self-Reference.Rohan French - 2016 - Ergo: An Open Access Journal of Philosophy 3.

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Citations of this work BETA

LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.
Structural Proof Theory for First-Order Weak Kleene Logics.Andreas Fjellstad - 2020 - Journal of Applied Non-Classical Logics 30 (3):272-289.
Logical Nihilism and the Logic of ‘Prem’.Andreas Fjellstad - forthcoming - Logic and Logical Philosophy:1.

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