The Logic of Categorial Grammars: A deductive account of natural language syntax and semantics (Lecture Notes in Computer Science, 6850)

Annotation This book is intended for students in computer science, formal linguistics, mathematical logic and to colleagues interested in categorial grammars and their logical foundations. These lecture notes present categorial grammars as deductive systems, in the approach called parsing-as-deduction, and the book includes detailed proofs of their main properties. The papers are organized in topical sections on AB grammars, Lambeks syntactic calculus, Lambek calculus and montague grammar, non-associative Lambek calculus, multimodal Lambek calculus, Lambek calculus, linear logic and proof nets and proof nets for the multimodal Lambek calculus -- Thistextbook is a contemporary, comprehensive introduction to categorial grammars in the logical tradition initiated by Lambek. It guides students and researchers through fundamental results, original developments and applications. Numerous examples and exercises underline the logical, computational and linguistic relevance of categorial grammars. Chapters: 1) AB grammars, 2) Lambek's Syntactic Calculus, 3) Lambek Calculus and Montague Grammar, 4) The non-associative Lambek calculus, 5) The multimodal Lambek calculus, 6) Proof nets for linear logic and the Lambek calculus, 7) Multimodal proof nets This textbook is a contemporary, comprehensive introduction to categorial grammars in the logical tradition initiated by Lambek. It guides students and researchers through fundamental results, original developments and applications. Numerous examples and exercises underline the logical, computational and linguistic relevance of categorial grammars. Chapters: 1) AB grammars, 2) Lambek's Syntactic Calculus, 3) Lambek Calculus and Montague Grammar, 4) The non-associative Lambek calculus, 5) The multimodal Lambek calculus, 6) Proof nets for linear logic and the Lambek calculus, 7) Multimodal proof nets. Front Matter....Pages - Classical Categorial Grammars: AB Grammars....Pages 1-22 A Logic for Categorial Grammars: Lambek’s Syntactic Calculus....Pages 23-63 Lambek Calculus and Montague Grammar....Pages 65-99 The Non-associative Lambek Calculus....Pages 101-147 The Multimodal Lambek Calculus....Pages 149-191 Lambek Calculus and Linear Logic: Proof Nets as Parse Structures....Pages 193-238 Proof Nets for the Multimodal Lambek Calculus: From Theory to a Wide-Coverage Categorial Parser....Pages 239-297 Back Matter....Pages -