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This chapter focuses on the Combinatory Categorial Grammar (CCG), a strongly lexicalized theory of grammar in which grammatical categories consist of a syntactic type defining valency, along with a logical form and a phonological form. It also discusses the Categorial Lexicon, the sole repository of language-specific information whose sounds and meanings are projected by a small universal set of type-driven combinatory syntactic rules onto the sounds and meanings of all and only the sentences of the language. CCG includes a number of restricted combinatory operations for combining categories that are strictly limited to various combinations of operations of type raising, composition, and substitution. Both reflexive/reciprocal binding and control are bounded under Condition A of the binding theory—that is, they relate elements within a single verbal domain. The chapter also examines relativization and relative pronouns, embedded subject extraction, pied-piping of wh-items such as which and who(m) in noun phrases, coordination of conjunctions, and the expressive power and computational complexity of CCG. Finally, it compares CCG with Categorial Type Logic and Lambek grammars.

This book has suggested that the only quantifier determiners in English with interpretations corresponding to generalized quantifiers are those which give rise to dependency-inducing scope inversion, do not combine with collective predicates such as gather in the library, exhibit singular agreement only, and are characterized by distributive conjunction. All other so-called quantifier determiners are entirely not quantificational, with the existentials instead denoting various types of individual, represented by generalized Skolem terms. The asymmetry with respect to collective verbs implies that English true quantifiers have no plural readings, at least in certain dialects. Under present assumptions, syntactic derivation in Combinatory Categorial Grammar alone, together with an “anytime” operation of Skolem term specification of the uninterpreted terms associated with indefinite noun phrases (NPs), can be used to directly compute the available scoped readings, including certain notorious cases involving inversion out of NPs.

Combinatory Categorial Grammar (CCG) allows semantically equivalent alternate surface derivations typified by the sentence “Harry admires Louise,” as well as English noun phrases, to have all of the type-raised categories allowed by a full-blown morphological case system. Many critics have argued that this so-called spurious ambiguity makes CCG quite impracticable to apply to useful tasks such as parsing and question answering in open domains, regardless of its linguistic attractions. This chapter examines how CCG can be used for efficient natural language processing. It first considers algorithms that have formed the basis of a number of practical CCG parsers before turning to logical forms and how they are built with CCG. The chapter also discusses processing scope and pronominal reference in CCG, generation of strings from logical forms using CCG, the use of scope for rapid inference in support of question answering or textual entailment, and human sentence processing.

Type raising, a rule of the Combinatory Categorial Grammar (CCG) lexicon, is the operation used by Richard Montague in 1973 in semantics to treat quantification in natural language and capture the phenomena of quantifier-scope illustrated by the sentence “Somebody loves everybody.” In this tradition, it is standard to translate expressions such as “every farmer” and “some donkey” into “generalized quantifiers.” This chapter discusses quantification and pronominal anaphora, explains how generalized quantifiers can be incorporated naturally into the semantics of CG determiners, and describes a category schema that makes generalized quantifiers function from nouns to type-raised noun phrases. It also discusses universal determiners and indefinite determiners, Skolem terms, definites, pronouns, and bound-variable anaphora.