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Differential Linear Logic and Polarization

  • Lionel Vaux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5608)

Abstract

We extend Ehrhard–Regnier’s differential linear logic along the lines of Laurent’s polarization. We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. Then we show this polarized differential linear logic refines the recently introduced convolution \({\bar\lambda}\mu\)-calculus, the same as linear logic decomposes λ-calculus.

Keywords

Classical Logic Linear Logic Reduction Rule Structural Rule Sequent Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Lionel Vaux
    • 1
  1. 1.Laboratoire de Mathématiques de l’Université de SavoieUMR 5127 CNRSLe Bourget-du-Lac CedexFrance

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