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Polarized Proof-Nets: Proof-Nets for LC

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Typed Lambda Calculi and Applications (TLCA 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1581))

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Abstract

We define a notion of polarization in linear logic (LL) coming from the polarities of Jean-Yves Girard’s classical sequent calculus LC [4]. This allows us to define a translation between the two systems. Then we study the application of this polar ization constraint to proofnets for full linear logic described in [7]. This yields an important simplification of the correctness criterion for polarized proof-nets. In this way we obtain a system of proof-nets for LC.

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References

  1. Vincent Danos, Jean-Baptiste Joinet, and Harold Schellinx. Computational isomorphisms in classical logic (extended abstract). In Jean-Yves Girard, Mitsu Okada, and Andr Scedrov, editors, Proceedings Linear Logic’ 96 Tokyo Meeting, volume 3 of Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam, 1996.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Luminy CNRS-Marseille, Marseille, France

    Olivier Laurent

Authors
  1. Olivier Laurent
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Editor information

Editors and Affiliations

  1. CNRS - UPR9016, Institut de Mathématiques de Luminy, 163 Avenue de Luminy, case 907, F-13288, Marseille cedex 9, France

    Jean-Yves Girard

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© 1999 Springer-Verlag Berlin Heidelberg

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Laurent, O. (1999). Polarized Proof-Nets: Proof-Nets for LC. In: Girard, JY. (eds) Typed Lambda Calculi and Applications. TLCA 1999. Lecture Notes in Computer Science, vol 1581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48959-2_16

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  • DOI: https://doi.org/10.1007/3-540-48959-2_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65763-7

  • Online ISBN: 978-3-540-48959-7

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