Advances in Linear Logic (London Mathematical Society Lecture Note Series, Series Number 222)

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. Contents......Page 5 Preface......Page 7 Linear Logic: its syntax and semantics......Page 9 Bilinear logic in algebra and linguistics......Page 51 A category arising in linear logic, complexity theory and set theory......Page 69 Hypercoherences: a strongly stable model of linear logic......Page 91 Deciding provability of linear logic formulas......Page 117 The direct simulation of Minsky machines in linear logic......Page 131 Stochastic interaction and linear logic......Page 155 Inheritance with exceptions......Page 175 On the fine structure of the exponential rule......Page 205 Sequent calculi for second order logic......Page 219 From proof nets to interaction nets......Page 233 Empires and kingdoms in MLL-......Page 257 Noncominutative proof nets......Page 279 Volume of mulitplica.tive formulas and provability......Page 305 Proof-nets and the Hilbert space......Page 315 Geometry of interaction III: accommodating the additives......Page 337 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.

This volume gives an overview of linear logic that will be useful to mathematicians and computer scientists working in this area.