Generalized Correspondence Analysis for Three-Valued Logics

Logica Universalis 12 (3-4):423-460 (2018)
Authors
Yaroslav Petrukhin
Moscow State University
Abstract
Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete analogue of LP, strong Kleene logic \. In this paper, we generalize these results for the negative fragments of LP and \, respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \, but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \ and its dual \ and LP).
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DOI 10.1007/s11787-018-0212-9
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - Journal of Philosophical Logic 44 (1):65-80.

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Logic Prizes Et Cætera.Jean-Yves Beziau - 2018 - Logica Universalis 12 (3-4):271-296.

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