Non-reflexive Nonsense: Proof-Theory for Paracomplete Weak Kleene Logic

Studia Logica (forthcoming)
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Abstract

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules.

Author Profiles

Bruno Da Re
Universidad de Buenos Aires (UBA)
Damian Szmuc
Universidad de Buenos Aires (UBA)

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