The weak equivalence of Combinatory Categorial Grammar (CCG) and Tree-Adjoining Grammar (TAG) is a central result of the literature on mildly context-sensitive grammar formalisms. However, the categorial formalism for which this equivalence has been established differs significantly from the versions of CCG that are in use today. In particular, it allows restriction of combinatory rules on a per grammar basis, whereas modern CCG assumes a universal set of rules, isolating all cross-linguistic variation in the lexicon. In this article we investigate the formal significance of this difference. Our main result is that lexicalized versions of the classical CCG formalism are strictly less powerful than TAG.

Psycholinguistic research shows that key properties of the human sentence processor are incrementality, connectedness (partial structures contain no unattached nodes), and prediction (upcoming syntactic structure is anticipated). There is currently no broad-coverage parsing model with these properties, however. In this article, we present the first broad-coverage probabilistic parser for PLTAG, a variant of TAG that supports all three requirements. We train our parser on a TAG-transformed version of the Penn Treebank and show that it achieves performance comparable to existing TAG parsers that are incremental but not predictive. We also use our PLTAG model to predict human reading times, demonstrating a better fit on the Dundee eye-tracking corpus than a standard surprisal model.