We propose a computational model for inducing full-fledged combinatory categorial grammars from behavioral data. This model contrasts with prior computational models of selection in representing syntactic and semantic types as structured (rather than atomic) objects, enabling direct interpretation of the modeling results relative to standard formal frameworks. We investigate the grammar our model induces when fit to a lexicon-scale acceptability judgment dataset – Mega Acceptability – focusing in particular on the types our model assigns to clausal complements and the predicates that select them.