Combinatory categorial grammars as generators of weighted forests

Combinatory Categorial Grammar (CCG) is an extension of categorial grammar that is well-established in computational linguistics. It is mildly context-sensitive, so it is efficiently parsable and reaches an expressiveness that is suitable for describing natural languages. Weighted CCG (wCCG) are introduced as a natural extension of CCG with weights taken from an arbitrary commutative semiring. Their expressive power is compared to other weighted formalisms with special emphasis on the weighted forests generated by wCCG since the ability to express the underlying syntactic structure of an input sentence is a vital feature of CCG in the area of natural language processing. Building on recent results for the expressivity in the unweighted setting, the corresponding results are derived for the weighted setting for any commutative semiring. More precisely, the weighted forests generatable by wCCG are also generatable by weighted simple monadic context-free tree grammar (wsCFTG). If the rule system is restricted to application rules and composition rules of first degree, then the generatable weighted forests are exactly the regular weighted forests. Finally, when only application rules are allowed, then a proper subset of the regular weighted forests is generatable.