Topos based semantic for constructive logic with strong negation

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Mathematical Logic Quarterly 38 (1):509-519 (1992)
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Abstract

The aim of the paper is to show that topoi are useful in the categorial analysis of the constructive logic with strong negation. In any topos ϵ we can distinguish an object Λ and its truth-arrows such that sets ϵ have a Nelson algebra structure. The object Λ is defined by the categorial counterpart of the algebraic FIDEL-VAKARELOV construction. Then it is possible to define the universal quantifier morphism which permits us to make the first order predicate calculus. The completeness theorem is proved using the Kripke-type semantic defined by THOMASON

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10.1002/malq.19920380146

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References found in this work

An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
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An Algebraic Approach to Non-Classical Logics.Anne Preller - 1977 - Journal of Symbolic Logic 42 (3):432-432.

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