Proof Theory of Paraconsistent Weak Kleene Logic

Studia Logica 108 (4):779-802 (2020)
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Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.



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Francesco Paoli
Universita di Cagliari

References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Time and modality.A. N. Prior - 1957 - Revue Philosophique de la France Et de l'Etranger 148:114-115.

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