Advances in Linear Logic [Paperback]

This volume gives an overview of linear logic that will be useful to mathematicians and computer scientists working in this area.Including a general introduction to linear logic that will ensure its use by the novice as well as the expert, this volume is divided into five parts: category theory; complexity and expressivity; proof theory; proof nets and the geometry of interaction.Including a general introduction to linear logic that will ensure its use by the novice as well as the expert, this volume is divided into five parts: category theory; complexity and expressivity; proof theory; proof nets and the geometry of interaction.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.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. Fouquer? 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 mlÃ&