Proofnets and Context Semantics for the Additives

  • Harry G. Mairson
  • Xavier Rival
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2471)

Abstract

We provide a context semantics for Multiplicative-Additive Linear Logic (MALL), together with proofnets whose reduction preserves semantics, where proofnet reduction is equated with cut-elimination on MALL sequents. The results extend the program of Gonthier, Abadi, and Lévy, who provided a “geometry of optimal λ-reduction” (context semantics) for λ-calculus and Multiplicative-Exponential Linear Logic (MELL). We integrate three features: a semantics that uses buses to implement slicing; a proofnet technology that allows multidimensional boxes and generalized garbage, preserving the linearity of additive reduction; and finally, a read-back procedure that computes a cut-free proof from the semantics, a constructive companion to full abstraction theorems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Harry G. Mairson
    • 1
  • Xavier Rival
    • 2
  1. 1.Computer Science DepartmentBrandeis University WalthamMassachusetts
  2. 2.École Normale SuperieureParis

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