About Translations of Classical Logic into Polarized Linear Logic

Abstract : We show that the decomposition of Intuitionistic Logic into Linear Logic along the equation A -> B = !A -o B may be adapted into a decomposition of classical logic into LLP, the polarized version of Linear Logic. Firstly we build a categorical model of classical logic (a Control Category) from a categorical model of Linear Logic by a construction similar to the co-Kleisli category. Secondly we analyse two standard Continuation-Passing Style (CPS) translations, the Plotkin and the Krivine's translations, which are shown to correspond to two embeddings of LLP into LL.
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Communication dans un congrès
Phokion G. Kolaitis. 2003, IEEE, pp.11-20, 2003, 〈10.1109/LICS.2003.1210040〉
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Contributeur : Olivier Laurent <>
Soumis le : mardi 27 septembre 2005 - 15:00:31
Dernière modification le : vendredi 4 janvier 2019 - 17:32:58

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Olivier Laurent, Laurent Regnier. About Translations of Classical Logic into Polarized Linear Logic. Phokion G. Kolaitis. 2003, IEEE, pp.11-20, 2003, 〈10.1109/LICS.2003.1210040〉. 〈hal-00009139〉

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