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Advances in Linear Logic



Advances in Linear Logic
Edited by Jean-Yves Girard, Yves Lafont and Laurent Regnier
Published by Cambridge University Press 1995
Paperback 24.95 pounds ISBN 0 521 55961 8

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, 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.

Contents:

    Linear logic: its syntax and semantics: J.Y. GIRARD;

 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;

 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 excepetions: C. FOUQUERE and J. VAUZEILLES;

 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;

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. Proof nets and Hilbert space: V. DANOS and L. REGNIER;
14. Geometry of interacion III: The general case: J.Y. GIRARD.

Further details can be obtained from the publisher by email  
science@cup.cam.ac.uk