Potoses: Categorical Paraconsistent Universum for Paraconsistent Logic and Mathematics


V. L. Vasyukov


It is well-known that the concept of da Costa algebra [3] reects most of the logical properties of paraconsistent propositional calculi $C_{n},1\leq n\leq \omega $ 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 $\textit{potos}$ { 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)
DOI: 10.21146/2074-1472-2017-23-2-76-95






Benabou, J. “Fibered Categories and the Foundations of Naive Category Theory”, The Journal of Symbolic Logic, 1983, Vol. 50, No. 4, pp. 9–37.
Caleiro, C., Gon_calves, R. “Behavioral algebraization of da Costa’s C-systems”, Journal of Applied Non-Classical Logics, 2009, Vol. 19, No. 2, pp. 127–148.
Carnielli, W.A., Alcantara, L.P. “Paraconsistent algebras”, Studia Logica, 1984, Vol. XLIII, No. 1/2, pp. 79–87.
da Costa, N.C.A. “Calculus propositionnels pour les systemes inconsistants”, C.R. Acad. Sci. Paris, 1963, T. 257, pp. 3790–3792.
da Costa, N.C.A. “Paraconsistent Mathematics”, in: Frontiers of Paraconsistent Logic, D. Batens et al. (eds.). Research Studies Press Ltd., Baldock, Hartfordshire, England, 2000, pp. 166–179.
da Costa, N.C.A., Alves, E.H. “A Semantical Analyses of the Calculi Cn”, Notre Dame Journal of Formal Logic, 1977, Vol. XVIII, No. 4, pp. 621–630.
Goldblatt, R. Toposes. The categorial analysis of logic. Amsterdam, North Holland, 1973.
Grishin, V.N. “Weight of the comprehension axiom in a theory based on logic without contractions”, Mathematical Notes, 1999, Vol. 66, No. 5, pp. 533–540.
Shepherdson, J.C. “Inner models for set theory”, Journal of Symbolic Logic, 1951, Vol. 15, pp. 161–190.
Vasyukov, V.L. “Paraconsistency in Categories”, in: Frontiers of Paraconsistent Logic, D. Batens, C. Mortensen, G. Priest and J.-P. van Bendegem (eds.). Research Studies Press Ltd., Baldock, Hartfordshire, England, 2000, pp. 263–278.
Vasyukov, V.L. Potosy dlya paraneprotivorechivoi logiki [Potoses for Paraconsistent Logics], Modern Logics: Issues of Theory, History and Implementation in Science. Papers from the X-th allRussian Scientific Conference, SPb, 2008. P. 105–107. (In Russian)