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.

Mark Steedman (2000).
The Syntactic Process,
MIT Press.

Mark Steedman (1996).
Surface Structure and Interpretation
(Linguistic Inquiry Monograph No. 30),
MIT Press.

Mark Steedman and Jason Baldridge (2003)
Combinatory Categorial Grammar
Unpublished Tutorial Paper. ps pdf

Mark Steedman (1999) Categorial Grammar,
MIT Encyclopedia of Cognitive Sciences,
R. Wilson and F. Keil (eds.) ps