Subtractive logic

Abstract : This paper is the first part of a work whose purpose is to investigate duality in some related frameworks (cartesian closed categories, lambda-calculi, intuitionistic and classical logics) from syntactic, semantical and computational viewpoints. We start with category theory and we show that any bicartesian closed category with coexponents is degenerated (i.e. there is at most one arrow between two objects). The remainder of the paper is devoted to logical issues. We examine the propositional calculus underlying the type system of bicartesian closed categories with coexponents and we show that this calculus corresponds to subtractive logic: a conservative extension of intuitionistic logic with a new connector (subtraction) dual to implication. Eventually, we consider first order subtractive logic and we present an embedding of classical logic into subtractive logic.
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Article dans une revue
Theoretical Computer Science, Elsevier, 2001, 254:1-2, pp.151-185
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https://hal.archives-ouvertes.fr/hal-00094589
Contributeur : Tristan Crolard <>
Soumis le : jeudi 14 septembre 2006 - 16:49:47
Dernière modification le : jeudi 17 mai 2018 - 12:52:03

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  • HAL Id : hal-00094589, version 1

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Tristan Crolard. Subtractive logic. Theoretical Computer Science, Elsevier, 2001, 254:1-2, pp.151-185. 〈hal-00094589〉

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