Outstanding Contributions to Logic

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

Editors: Casadio, Claudia, Scott, Philip J. (Eds.)

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  • Discusses J. Lambek’s groundbreaking works in mathematics, logic, linguistics, and theoretical computer science 
  • Surveys the fundamental influence of Lambek’s methods in algebra, proof theory, and computability 
  • Explores Lambek’s seminal ideas on linear logics, vector space models of grammar, and categorical models of language
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About this book

This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. 

After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory).  In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability.  In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics.   

This book is of interest to mathematicians, logicians, linguists, and computer scientists.

About the authors

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).

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-66545-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-030-66544-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
Editors
  • Claudia Casadio
  • Philip J. Scott
Series Title
Outstanding Contributions to Logic
Series Volume
20
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-66545-6
DOI
10.1007/978-3-030-66545-6
Hardcover ISBN
978-3-030-66544-9
Series ISSN
2211-2758
Edition Number
1
Number of Pages
XXXII, 432
Number of Illustrations
1 b/w illustrations
Topics