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• W2912464567 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." @default.
• W2912464567 created "2019-02-21" @default.
• W2912464567 creator A5007146319 @default.
• W2912464567 date "2001-03-01" @default.
• W2912464567 modified "2023-10-17" @default.
• W2912464567 title "Subtractive logic" @default.
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• W2912464567 doi "https://doi.org/10.1016/s0304-3975(99)00124-3" @default.
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