In syntactic parsing, proof nets are graphical structures that have the advantageous property of invariance to spurious ambiguities. Semantically-equivalent derivations correspond to a single proof net. Recent years have seen fresh interest in statistical syntactic parsing with proof nets, including the development of methods based on neural networks. However, training of statistical parsers requires corpora that provide ground-truth syntactic analyses. Unfortunately, there has been a paucity of corpora in formalisms for which proof nets are applicable, such as Lambek categorial grammar (LCG), a formalism related to combinatory categorial grammar (CCG). To address this, we leverage CCGbank and the relationship between LCG and CCG to develop LCGbank, an English-language corpus of syntactic analyses based on LCG proof nets. In contrast to CCGbank, LCGbank eschews type-changing and uses only categorial rules; the syntactic analyses thus provide fully compositional semantics, exploiting the transparency between syntax and semantics that so characterizes categorial grammars.

The title of this book, Categorial Grammar: Logical Syntax, Semantics, and Processing, indicates that this will be a book about categorial grammar.In the preface, however, several strains of categorial grammar are discussed, including combinatory categorial grammar (Steedman 2000), pregroup grammar (Lambek 1999), and abstract categorial grammar (de Groote 2001), and it is clarified that the book investigates only the tradition of type-logical grammar, or rather, those grammars based on Lambek categorial grammar (Lambek 1958).That being said, this book contains a good introduction to type-logical grammar and its first part would make a good textbook in an advanced course on the theory of type-logical grammar.In particular, exercises are sprinkled throughout the book that will be illuminating to the uninitiated reader.The book is neatly divided into three parts that are likely to be of varying levels of interest depending on the specific audience.Part I, titled "Lambek Categorial Grammar," gives a concise introduction to a number of aspects of Lambek categorial grammar, which is suitable for an audience interested in the basic intuitions and mechanics of that grammar.Part II, titled "Logical Categorial Grammar," introduces a number of extensions of Lambek's grammar, each of which are motivated by linguistic considerations.This part is likely to be of relevance to linguists who are interested in the descriptive capabilities of type-logical grammar, but little attention is paid to computational aspects in this part.Part III is a collection of remaining topics that are loosely connected by their attention to processing.This part is directed towards those interested in psycho-linguistics and its connections to type-logical grammars.Section 1 of Part I introduces the origin of type-logical grammar, which is found in the grammar of Ajdukiewicz (1935) and connected to Montague's semantics (Montague and Thomason 1974).Section 2 introduces the syntax of Lambek categorial grammar, including the introduction of both a proof theory and a model theory.This section then discusses the cut elimination proof for the Lambek calculus, the logical system behind Lambek categorial grammar.Section 3 introduces the semantics for Lambek categorial grammar, including a discussion of the Curry-Howard isomorphism and its relevance to Lambek categorial grammar.Both Sections 2 and 3 include example sentences from English and analyses for those sentences that give the reader an insight into how typelogical grammar is applied to linguistic data.Section 4, titled "Processing," introduces proof nets for Lambek categorial grammar as a more natural representation of typelogical syntax and semantics.Human performance on garden-path sentences is used to motivate the use of both proof nets, in particular, and type-logical grammar, more generally.