Paraconsistent Logic for Dialethic Arithmetics
Andrew Tedder · ERA: Education and Research Archive (University of Alberta) · 2014
Inconsistent and collapse models of arithmetic are presented in the language and semantics of the simple paraconsistent logic LP. I present a logic which extends LP by the addition of a sensible conditional connective and quantifiers. This logic, called A 3 , is specified as a Hilbert style axiom system and a Gentzen-style sequent calculus, and these systems are shown to be equivalent. I show the sequent calculus to be sound and complete for the A3 semantics and prove the elimination theorem. Finally, I specify arithmetical axiom systems for the collapse models and show that these axiom systems capture some salient properties of their associated models.