Moot R., Retoré C. The Logic of Categorial Grammars. A Deductive Account of Natural Language Syntax and Semantics

Springer, 2012. — 322 p.This book is intended for students (from the third year) in computer science, formal linguistics, and mathematical logic as well as for colleagues interested in categorial grammars and their logical foundations. Though the logical viewpoint of categorial grammars is well-established, until now there has been no textbook available to students and researchers who want to discover all the main results for categorial grammars. It is the goal of this book to fill this gap.
The book has few formal prerequisites; nevertheless, notions of mathematical logic will help.
In addition, some familiarity with proof theory and the typed -calculus will help, and for readers who feel they need additional background we recommend (Girard et al, 1988; Girard, 2011), and (Girard, 1995, 2011) for more details on linear logic.
Occasionally, we will assume the reader knows what context-free grammar is,
and is aware of their elementary properties such as Chomsky and Greibach normal forms. If some background on formal language theory is needed, we recommend (Hopcroft and Ullman, 1979; Harrison, 1978)
Finally, for some background in linguistics, we recommend (Akmajian et al, 2001).
Nevertheless we have made every effort to make this book as self-contained as possible, and none of this additional background knowledge is strictly mandatory.
The exercises at the end of every chapter, sometimes with hints, should help the reader assimilate the new notions and check that they are well understood.
These lecture notes present categorial grammars as deductive systems, in the approach called parsing-as-deduction, and we include detailed proofs of their main properties. We provide background and motivation for all results, modern proofs of many of the classical results for categorial grammars, together with our own results, in particular on proof nets.Classical Categorial Grammars: AB Grammars
A Logic for Categorial Grammars: Lambek’s Syntactic Calculus
Lambek Calculus and Montague Grammar
The Non-associative Lambek Calculus
The Multimodal Lambek Calculus
Lambek Calculus and Linear Logic: Proof Nets as Parse Structures
Proof Nets for the Multimodal Lambek Calculus: From Theory to aWide-Coverage Categorial Parser