Linear Logic, -Autonomous Categories and Cofree Coalgebras (1989) [85 citations — 7 self]
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author = {R.A.G. Seely},
title = {Linear Logic, -Autonomous Categories and Cofree Coalgebras},
booktitle = {In Categories in Computer Science and Logic},
year = {1989},
pages = {371--382},
publisher = {American Mathematical Society}
}
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Abstract:
. A brief outline of the categorical characterisation of Girard's linear logic is given, analagous to the relationship between cartesian closed categories and typed -calculus. The linear structure amounts to a -autonomous category: a closed symmetric monoidal category G with finite products and a closed involution. Girard's exponential operator, ! , is a cotriple on G which carries the canonical comonoid structure on A with respect to cartesian product to a comonoid structure on !A with respect to tensor product. This makes the Kleisli category for ! cartesian closed. 0. INTRODUCTION. In "Linear logic" [1987], Jean-Yves Girard introduced a logical system he described as "a logic behind logic". Linear logic was a consequence of his analysis of the structure of qualitative domains (Girard [1986]): he noticed that the interpretation of the usual conditional ")" could be decomposed into two more primitive notions, a linear conditional "\Gammaffi" and a unary operator "!" (called "of cours...
Citations
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