Differential Linear Logic and Polarization

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


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.


Classical Logic Linear Logic Reduction Rule Structural Rule Sequent Calculus 
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© 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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