Linear logic in computer science

✍ Scribed by Thomas Ehrhard, Jean-Yves Girard, Paul Ruet, Philip Scott

• Publisher: Cambridge University Press
• Year: 2004
• Tongue: English
• Leaves: 392
• Series: London Mathematical Society lecture note series 316
• Category: Library

✦ Synopsis

Linear Logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area.

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
List of contributors......Page 10
Part one: Tutorials......Page 12
1 Category Theory for Linear Logicians R. Blute and Ph. Scott......Page 14
2 Proof Nets and the A-Calculus S. Guerrini......Page 76
3 An Overview of Linear Logic Programming D. Miller......Page 130
4 Linearity and Nonlinearity in Distributed Computation G. Winskel......Page 162
Part two: Refereed Articles......Page 200
5 An Axiomatic Approach to Structural Rules for Locative Linear Logic J.-M. Andreoli......Page 202
6 An Introduction to Uniformity in Ludics C. Faggian, M.-R. Fleury-Donnadieu and M. Quatrini......Page 247
7 Slicing Polarized Additive Normalization 0. Laurent, L. Tortora de Falco......Page 258
8 A Topological Correctness Criterion for Multiplicative Non-Commutative Logic P.-A. Mellies......Page 294
Part three: Invited Articles......Page 334
9 Bicategories in Algebra and Linguistics J. Lambek......Page 336
10 Between Logic and Quantic: a Tract J.-Y. Girard......Page 357