Combinatory categorial grammar
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Combinatory categorial grammar (CCG) is an efficiently parseable, yet linguistically expressive grammar formalism. It has a completely 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.
[edit] 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.
