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Article Dans Une Revue Annals of Pure and Applied Logic Année : 2005

Polarized and focalized linear and classical proofs

Olivier Laurent
Myriam Quatrini
Lorenzo Tortora de Falco
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Résumé

We give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs are at the heart of our analysis: we show that the tq-protocol of normalization for the classical systems LKeta,pol and LKeta,rho,pol perfectly fits normalization of polarized proof-nets. Some more semantical considerations allow us to recover LC as a refinement of multiplicative LKeta,pol.

Dates et versions

hal-00009133 , version 1 (27-09-2005)

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Olivier Laurent, Myriam Quatrini, Lorenzo Tortora de Falco. Polarized and focalized linear and classical proofs. Annals of Pure and Applied Logic, 2005, 134, pp.217-264. ⟨10.1016/j.apal.2004.11.002⟩. ⟨hal-00009133⟩
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