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Proofnets and Context Semantics for the Additives

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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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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Author information

Authors and Affiliations

  1. Computer Science Department, Brandeis University Waltham, Massachusetts, 02454

    Harry G. Mairson

  2. École Normale Superieure, 45 rue d’Ulm, 75005, Paris

    Xavier Rival

Authors
  1. Harry G. Mairson
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  2. Xavier Rival
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Editor information

Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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© 2002 Springer-Verlag Berlin Heidelberg

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Mairson, H.G., Rival, X. (2002). Proofnets and Context Semantics for the Additives. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_11

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  • DOI: https://doi.org/10.1007/3-540-45793-3_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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