Паранепротиворечивые категории для паранепротиворечивой логики

Abstract

It is well known that the concept of da Costa algebra [4] reflects most of the logical properties of paraconsistent propositional calculi $C_n$ ($1 \leq n \leq \omega$) introduced by N.C.A. da Costa. In [8] 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). In the paper the potos completeness of da Costa logics (i.e. in respect to the potoses) is proved.