Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics
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Beschreibung
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.
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.
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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Themen in »Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics«
Category theory and Algebra Categorical Proof Theory and Coherence Monoidal and Mal’cev Categories Sheaf Representation and Duality Categorical Recursion Theory Lambda Calculi and Dependent Types Noncommutative Linear Logics, Pomset logics, and Proof Nets Lambek Grammars and their extensions Lambek’s Pregroup models of linguistics Noncommutative Variants of Linear Logic Laws and Proof-Nets Sheaf Representations and Duality in Logic naturalness of Maltsev categories Extensions of Lambek Calculi Mathematics of Text Structure