Logic Of Categorial Grammars

The papers are organized in topical sections on AB grammars, Lambek’s 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. 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. 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, Lambek’s 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.