Semantic bootstrapping of type-logical grammar

A two-stage procedure is described which induces type-logical grammar lexicons from sentences annotated with skeletal terms of the simply typed lambda calculus. First, a generalized formulae-as-types correspondence is exploited to obtain all the type-logical proofs of the sample sentences from their lambda terms. The resulting lexicons are then optimally unified. The first stage constitutes the semantic bootstrapping, while the unification procedure of Buszkowski and Penn represents a first attempt at structure-dependent distributional learning of the syntactic and semantic categories. This effort extends earlier induction procedures for classical categorial grammar to at first the non-associative Lambek calculus, and then to a large class of type logics enriched by modal operators and structural rules.