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Categories and Types in Logic, Language, and Physics

Essays dedicated to Jim Lambek on the Occasion of this 90th Birthday

  • Book
  • © 2014

Overview

Editors:
  1. Claudia Casadio

    1. Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti, Italy

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  2. Bob Coecke

    1. Department of Computer Science, Oxford University, Oxford, UK

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  3. Michael Moortgat

    1. Utrecht Institute of Linguistics OTS, Utrecht University, Utrecht, The Netherlands

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  4. Philip Scott

    1. Department of Mathematics, University of Ottawa, Ottawa, Canada

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  • Dedicated to Jim Lambek, a profoundly inspirational mathematician, whose contributions cover an extraordinarily large range of topics, from mathematics to linguistics to physics
  • Contains papers by leading researchers in the fields of algebra, category theory, linguistics, theoretical physics, logic and proof theory
  • Preface contains some personal recollections, describing different ways the editors of this book have come to know Jim Lambek

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 8222)

Part of the book sub series: Theoretical Computer Science and General Issues (LNTCS)

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Table of contents (23 chapters)

  1. Front Matter

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  2. Semantic Unification

    • Samson Abramsky, Mehrnoosh Sadrzadeh
    Pages 1-13

  3. On Residuation

    • V. Michele Abrusci
    Pages 14-27

  4. Type Similarity for the Lambek-Grishin Calculus Revisited

    • Arno Bastenhof
    Pages 28-50

  5. NP-Completeness of Grammars Based Upon Products of Free Pregroups

    • Denis Béchet
    Pages 51-62

  6. Distributional Semantics: A Montagovian View

    • Raffaella Bernardi
    Pages 63-89

  7. A Logical Basis for Quantum Evolution and Entanglement

    • Richard F. Blute, Alessio Guglielmi, Ivan T. Ivanov, Prakash Panangaden, Lutz Straßburger
    Pages 90-107

  8. Learning Lambek Grammars from Proof Frames

    • Roberto Bonato, Christian Retoré
    Pages 108-135

  9. Multi-Sorted Residuation

    • Wojciech Buszkowski
    Pages 136-155

  10. Italian Clitic Patterns in Pregroup Grammar: State of the Art

    • Claudia Casadio, Aleksandra Kiślak-Malinowska
    Pages 156-171

  11. On Associative Lambek Calculus Extended with Basic Proper Axioms

    • Annie Foret
    Pages 172-187

  12. Classical Structures Based on Unitaries

    • Peter Hines
    Pages 188-210

  13. Initial Algebras of Terms with Binding and Algebraic Structure

    • Bart Jacobs, Alexandra Silva
    Pages 211-234

  14. Abstract Tensor Systems as Monoidal Categories

    • Aleks Kissinger
    Pages 235-252

  15. On Canonical Embeddings of Residuated Groupoids

    • Mirosława Kołowska-Gawiejnowicz
    Pages 253-267

  16. L-Completeness of the Lambek Calculus with the Reversal Operation Allowing Empty Antecedents

    • Stepan Kuznetsov
    Pages 268-278

  17. A Note on Multidimensional Dyck Languages

    • Michael Moortgat
    Pages 279-296

  18. Extended Lambek Calculi and First-Order Linear Logic

    • Richard Moot
    Pages 297-330

  19. A Categorial Type Logic

    • Glyn Morrill
    Pages 331-352

  20. Chasing Diagrams in Cryptography

    • Dusko Pavlovic
    Pages 353-367
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti, Italy

    Claudia Casadio

  • Department of Computer Science, Oxford University, Oxford, UK

    Bob Coecke

  • Utrecht Institute of Linguistics OTS, Utrecht University, Utrecht, The Netherlands

    Michael Moortgat

  • Department of Mathematics, University of Ottawa, Ottawa, Canada

    Philip Scott

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