Logical Investigations 20:255-268 (2014)

Allard Tamminga
University of Greifswald
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.
Keywords Three-valued logic  Correspondence analysis  Natural deduction
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References found in this work BETA

On Notation for Ordinal Numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.

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Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.

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