Potoses: Categorical Paraconsistent Universum for Paraconsistent Logic and Mathematics

Abstract

It is well-known that the concept of da Costa algebra [3] reflects most of the logical properties of paraconsistent propositional calculi C n , 1 ≤ n ≤ ω introduced by N.C.A. da Costa. In [10] the construction of topos of functors from a small category to the category of sets was proposed which allows to yield the categorical semantics for da Costa's paraconsistent logic. Another categorical semantics for C n would be obtained by introducing the concept of potos -the categorical counterpart of da Costa algebra (the name "potos" is borrowed from W.Carnielli's story of the idea of such kind of categories)