Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics

Claudia Casadio is Full Professor in Logic and Philosophy of Science at the University G. D'Annunzio, Chieti–Pescara, in the Department of Modern Languages, Literatures and Cultures.  Her research focuses on language and thinking, in particular: linguistic and cognitive categories, formal properties of natural language, human reasoning, interaction of formal, and mathematical vs. concrete thinking.  Philip Scott is Emeritus Full Professor, Department of Mathematics and Statistics, University of Ottawa.  His interests include categorical logic and algebra, proof theory, linear logic, and theoretical computer science.  He is a senior editor of two major journals in these areas.  He was a long-time collaborator of J. Lambek and the co-author of their well-known book Introduction to Higher Order Categorical Logic (1986).

• Chapter 1. Introduction (Joachim Lambek).- Chapter 2. Lambek’s Syntactic Calculus and Noncommutative Variants of Linear Logic: Laws and Proof-Nets (Michele Abrusci).- Chapter 3. Sheaf Representations and Duality in Logic (Steve Awodey).- Chapter 4. On the naturalness of Maltsev categories (D. Bourn).- Chapter 5. Extensions of Lambek Calculi (Wojciech Buszkowski).- Chapter 6. Categories with Families: Unityped, Simply Typed, and Dependently Typed (Simon Castellan).- Chapter 7. The Mathematics of Text Structure (Bob Coecke).- Chapter 8. Aspects of Categorical Recursion Theory (Pieter Hofstra).- Chapter 9. Pomset logic: another approach to non commutativity in logic (Christian Retoré).- Chapter10. Morphisms of Rings (Robert Paré).- Chapter 11. Pregroup Grammars, their Syntax and Semantics (Mehrnoosh Sadrzadeh).- Chapter 12. The Sequent Calculus of Skew Monoidal Categories (Tarmo Uustalu).