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