Abstract
The essential interaction between classical and intuitionistic features in the system of linear logic is best described in the language of category theory. Given a symmetric monoidal closed category C with products, the category C×Cop can be given the structure of a *-autonomous category by a special case of the Chu construction. The main result of the paper is to show that the intuitionistic translations induced by Girard’s trips determine the functor from the free *-autonomous category A on a set of atoms {P,P′,...} to C × Cop, where C is the free monoidal closed category with products and coproducts on the set of atoms {P O , P I , P′ O , P′ I ,...} (a pair P O , P I in C for each atom P of A).
Research supported by EPSRC senior research fellowship on grant GL/L 33382. We wish to thank Martin Hyland for his essential suggestions and crucial support in the develoment of this work.
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Bellin, G. (2003). Chu’s Construction: A Proof-Theoretic Approach. In: de Queiroz, R.J.G.B. (eds) Logic for Concurrency and Synchronisation. Trends in Logic, vol 15. Springer, Dordrecht. https://doi.org/10.1007/0-306-48088-3_2
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