The formalism generates constituency-based structures (as opposed to dependency-based ones) and is therefore a type of phrase structure grammar (as opposed to a dependency grammar).
The first linguistic and psycholinguistic arguments for basing the grammar on combinators were put forth by Steedman and Szabolcsi.
More recent prominent proponents of the approach are Pauline Jacobson and Jason Baldridge.
In these new approaches, the combinator B (the compositor) is useful in creating long-distance dependencies, as in "Who do you think Mary is talking about?"
and the combinator W (the duplicator) is useful as the lexical interpretation of reflexive pronouns, as in "Mary talks about herself".
Together with I (the identity mapping) and C (the permutator) these form a set of primitive, non-interdefinable combinators.
The CCG formalism defines a number of combinators (application, composition, and type-raising being the most common).
These operate on syntactically-typed lexical items, by means of Natural deduction style proofs.
The goal of the proof is to find some way of applying the combinators to a sequence of lexical items until no lexical item is unused in the proof.
The sentence "the dog bit John" has a number of different possible proofs.
The variety of proofs demonstrates the fact that in CCG, sentences don't have a single structure, as in other models of grammar.
Let the types of these lexical items be We can perform the simplest proof (changing notation slightly for brevity) as: Opting to type-raise and compose some, we could get a fully incremental, left-to-right proof.
The ability to construct such a proof is an argument for the psycholinguistic plausibility of CCG, because listeners do in fact construct partial interpretations (syntactic and semantic) of utterances before they have been completed.
Kuhlmann et al. (2015)[2] show that this equivalence, and the ability of CCG to describe
, rely crucially on the ability to restrict the use of the combinatory rules to certain categories, in ways not explained above.