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Theses

Étude de la polarisation en logique

Abstract : Coming from the study of linear logic and from the computational analysis of classical logic, the notion of polarities seems to have a very important place in the recent study of logical systems. The polarization constraint simplifies objects without reducing the computational expressivity too much.

This thesis deals with the study of this new structure given by polarities in order to enlighten the relations between classical logic and linear logic (LL). The introduction of polarities in LL allows to better understand this complex system. In particular, we define for this polarized linear logic (LLP): a notion of proof-nets dealing with the additive connectives, a polarized game
semantics reconciliating games and duality, a parallel geometry of interaction and some other denotational semantics based on already known structures (correlation spaces, control categories).

An important point is that LLP is still expressive enough. We precisely study the translations of the various deterministic systems for classical logic (LC, lambda-mu calculus, ...) both for call-by-name evaluation and for call-by-value. Moreover these translations are simpler than translations of the classical systems into LL.

These simplified translations allow to precisely analyze in LLP some properties of classical logic as LL allows to analyze intuitionistic logic. In particular it is possible to study a linear equivalent of CPS-translations.
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https://tel.archives-ouvertes.fr/tel-00007884
Contributor : Olivier Laurent <>
Submitted on : Monday, January 3, 2005 - 4:19:10 PM
Last modification on : Friday, September 28, 2018 - 4:06:02 PM
Long-term archiving on: : Thursday, September 13, 2012 - 1:55:34 PM

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Olivier Laurent. Étude de la polarisation en logique. Mathématiques [math]. Université de la Méditerranée - Aix-Marseille II, 2002. Français. ⟨tel-00007884⟩

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