Categories and Types in Logic, Language, and Physics

For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek’s work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek’s ideas keep inspiring upcoming generations of scholars.

Table of Contents

Chapter 1. Semantic Unification A Sheaf Theoretic Approach to Natural Language
Chapter 2. On Residuation
Chapter 3. Type Similarity for the Lambek-Grishin Calculus Revisited
Chapter 4. NP-Completeness of Grammars Based Upon Products of Free Pregroups
Chapter 5. Distributional Semantics: A Montagovian View
Chapter 6. A Logical Basis for Quantum Evolution and Entanglement
Chapter 7. Learning Lambek Grammars from Proof Frames
Chapter 8. Multi-Sorted Residuation
Chapter 9. Italian Clitic Patterns in Pregroup Grammar: State of the Art
Chapter 10. On Associative Lambek Calculus Extended with Basic Proper Axioms
Chapter 11. Classical Structures Based on Unitaries
Chapter 12. Initial Algebras of Terms with Binding and Algebraic Structure
Chapter 13. Abstract Tensor Systems as Monoidal Categories
Chapter 14. On Canonical Embeddings of Residuated Groupoids
Chapter 15. L-Completeness of the Lambek Calculus with the Reversal Operation Allowing Empty Antecedents
Chapter 16. A Note on Multidimensional Dyck Languages
Chapter 17. Extended Lambek Calculi and First-Order Linear Logic
Chapter 18. A Categorial Type Logic
Chapter 19. Chasing Diagrams in Cryptography
Chapter 20. The Monotone Lambek Calculus Is NP-Complete
Chapter 21. A Mathematical Analysis of Masaccio’s Trinity
Chapter 22. Conjoinability in 1-Discontinuous Lambek Calculus
Chapter 23. The Hidden Structural Rules of the Discontinuous Lambek Calculus