Advances in Linear Logic - Brossura

Based to a large extent on the Linear Logic Workshop held at Cornell, in June 1993, this volume aims to give an overview of linear logic that will be useful to mathematicians and computer scientists working in this area. The book is in five parts: categories and semantics; complexity and expressivity; proof theory; proof nets; and geometry of interaction. The whole book begins with a general introduction on linear logic which should ensure that this book can be used by the novice as well as the expert.

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.