Advances in Linear Logic

by Jean-Yves Girard, Yves Lafont, Laurent Regnier

Overview

This volume gives an overview of linear logic in five parts: category theory; complexity and expressivity; proof theory; proof nets; and the geometry of interaction. The book includes a general introduction to linear logic that will ensure this book's use by the novice as well as the expert. Mathematicians and computer scientists will learn much from this book.

Product Details

ISBN-13:	9780521559614
Publisher:	Cambridge University Press
Publication date:	06/22/1995
Series:	London Mathematical Society Lecture Note Series , #222
Pages:	400
Product dimensions:	6.02(w) x 8.90(h) x 0.91(d)

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.