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Advances in Linear Logic

Advances in Linear Logic

Part of London Mathematical Society Lecture Note Series

  • Editors:
  • Jean-Yves Girard, Centre National de la Recherche Scientifique (CNRS), Paris
  • Yves Lafont, Centre National de la Recherche Scientifique (CNRS), Paris
  • Laurent Regnier, Centre National de la Recherche Scientifique (CNRS), Paris
J. Y. Girard, J. Lambek, A. Blass, T. Erhard, P. D. Lincoln, M. I. Kanovich, J. Mitchell, A. Scedrov, C. Fouqueré, J. Vauzeilles, S. Martini, A. Masini, V. Danos, J. B. Joinet, H. Schellinx, Y. Lafont, G. Bellin, J. Van De Wiele, V. M. Abrusci, F. Metayer
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  • Date Published: June 1995
  • availability: Available
  • format: Paperback
  • isbn: 9780521559614

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  • Linear logic, introduced in 1986 by J.-Y. Girard, is based upon a fine grain analysis of the main proof-theoretical notions of logic. The subject develops along the lines of denotational semantics, proof nets and the geometry of interaction. Its basic dynamical nature has attracted computer scientists, and various promising connections have been made in the areas of optimal program execution, interaction nets and knowledge representation. This book is the refereed proceedings of the first international meeting on linear logic held at Cornell University, in June 1993. Survey papers devoted to specific areas of linear logic, as well as an extensive general introduction to the subject by J.-Y. Girard, have been added, so as to make this book a valuable tool both for the beginner and for the advanced researcher.

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    Product details

    • Date Published: June 1995
    • format: Paperback
    • isbn: 9780521559614
    • length: 400 pages
    • dimensions: 229 x 152 x 23 mm
    • weight: 0.59kg
    • availability: Available
  • Table of Contents

    Linear logic: its syntax and semantics J. Y. Girard
    Part I. Categories and Semantics:
    1. Bilinear logic in algebra and linguistics J. Lambek
    2. A category arising in linear logic, complexity theory and set theory A. Blass
    3. Hypercoherences: a strongly stable model of linear logic T. Erhard
    Part II. Complexity and Expressivity:
    4. Deciding provability of linear logic formulas P. D. Lincoln
    5. The direct simulation of Minsky machines in linear logic M. I. Kanovich
    6. Stochastic interaction and linear logic P. D. Lincoln, J. Mitchell and A. Scedrov
    7. Inheritance with exceptions C. Fouqueré and J. Vauzeilles
    Part III. Proof Theory:
    8. On the fine structure of the exponential rule S. Martini and A. Masini
    9. Sequent calculi for second order logic V. Danos, J. B. Joinet and H. Schellinx
    Part IV. Proff Nets:
    10. From proof nets to interaction nets Y. Lafont
    11. Empires and kingdoms in MLL G. Bellin and J. Van De Wiele
    12. Noncommutative proof nets V. M. Abrusci
    13. Volume of multiplicative formulas and provability F. Metayer
    Part V. Geometry of Interaction:
    14. Proof nets and Hilbert space V. Danos and L. Regnier
    15. Geometry of interacion III: accomodating the additives J. Y. Girard.

  • Editors

    Jean-Yves Girard, Centre National de la Recherche Scientifique (CNRS), Paris

    Yves Lafont, Centre National de la Recherche Scientifique (CNRS), Paris

    Laurent Regnier, Centre National de la Recherche Scientifique (CNRS), Paris

    Contributors

    J. Y. Girard, J. Lambek, A. Blass, T. Erhard, P. D. Lincoln, M. I. Kanovich, J. Mitchell, A. Scedrov, C. Fouqueré, J. Vauzeilles, S. Martini, A. Masini, V. Danos, J. B. Joinet, H. Schellinx, Y. Lafont, G. Bellin, J. Van De Wiele, V. M. Abrusci, F. Metayer

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