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Communication Dans Un Congrès Année : 2003

About Translations of Classical Logic into Polarized Linear Logic

Olivier Laurent
Laurent Regnier

Résumé

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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Dates et versions

hal-00009139 , version 1 (27-09-2005)

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Olivier Laurent, Laurent Regnier. About Translations of Classical Logic into Polarized Linear Logic. 2003, pp.11-20, ⟨10.1109/LICS.2003.1210040⟩. ⟨hal-00009139⟩
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