Correspondence analysis for strong three-valued logic
Logical Investigations 20:255-268 (2014)
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Abstract |
I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural deduction systems is sound and complete with respect to its particular
semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic.
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Keywords | Three-valued logic Correspondence analysis Natural deduction |
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Note on 'Normalisation for Bilateral Classical Logic with Some Philosophical Remarks'.Nils Kürbis - 2021 - Journal of Applied Logics 7 (8):2259-2261.
Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox.Yaroslav Petrukhin & Vasily Shangin - 2017 - Review of Symbolic Logic 10 (4):756-781.
Generalized Correspondence Analysis for Three-Valued Logics.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (3-4):423-460.
Automated Proof-Searching for Strong Kleene Logic and its Binary Extensions Via Correspondence Analysis.Yaroslav Petrukhin & Vasilyi Shangin - forthcoming - Logic and Logical Philosophy:1.
Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
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