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Advances in Linear Logic

Advances in Linear Logic

Advances in Linear Logic

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
August 1995
Paperback
9780521559614
NZD$113.95
inc GST
Paperback
USD
eBook

    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

    August 1995
    Paperback
    9780521559614
    400 pages
    226 × 153 × 23 mm
    0.57kg
    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.
      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

    • 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