Combinatory categorial grammar

Combinatory categorial grammar (CCG) is an efficiently parseable, yet linguistically expressive grammar formalism. It has a transparent interface between surface syntax and underlying semantic representation, including predicate-argument structure, quantification and information structure.

CCG relies on combinatory logic, which has the same expressive power as the lambda calculus, but builds its expressions differently. 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 Jacobson and Baldridge.

For example, 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. Jacobson interprets personal pronouns as the combinator I, and their binding is aided by a complex combinator Z, as in "Mary lost her way". Z is definable using W and B.

Formal properties

This section requires expansion.

CCG is known to define the same language class as tree-adjoining grammar, linear indexed grammar, and head grammar, and is said to be mildly context-sensitive.

References

• Baldridge, Jason (2002), "Lexically Specified Derivational Control in Combinatory Categorial Grammar." PhD Dissertation. Univ. of Edinburgh.
• Curry, Haskell B. and Richard Feys (1958), Combinatory Logic, Vol. 1. North-Holland.
• Jacobson, Pauline (1999), “Towards a variable-free semantics.” Linguistics and Philosophy 22, 1999. 117-184
• Steedman, Mark (1987), “Combinatory grammars and parasitic gaps”. Natural Language and Linguistic Theory 5, 403-439.
• Steedman, Mark (1996), Surface Structure and Interpretation. The MIT Press.
• Steedman, Mark (2000), The Syntactic Process. The MIT Press.
• Szabolcsi, Anna (1989), "Bound variables in syntax (are there any?)." Semantics and Contextual Expression, ed. by Bartsch, van Benthem, and van Emde Boas. Foris, 294-318.
• Szabolcsi, Anna (1992), "Combinatory grammar and projection from the lexicon." Lexical Matters. CSLI Lecture Notes 24, ed. by Sag and Szabolcsi. Stanford, CSLI Publications. 241-269.
• Szabolcsi, Anna (2003), “Binding on the fly: Cross-sentential anaphora in variable-free semantics”. Resource Sensitivity in Binding and Anaphora, ed. by Kruijff and Oehrle. Kluwer, 215-229.

Further reading

• Michael Moortgat, Categorial Type Logics, Chapter Two in J. van Benthem and A. ter Meulen (eds.) Handbook of Logic and Language. Elsevier, 1997, ISBN 0262220539

External links

• The Combinatory Categorial Grammar Site
• The ACL CCG wiki page (likely to be more up-to-date than this one)