International audienceWe study languages of λ-terms generated by IO and OI unsafe grammars. These languages can be used to model meaning representations in the formal semantics of natural languages following the tradition of Montague [25]. Using techniques pertaining to the denotational semantics of the simply typed λ-calculus, we show that the emptiness and membership problems for both types of grammars are decidable. In the course of the proof of the decidability results for OI, we identify a decidable variant of the λ-definability problem, and prove a stronger form of Statman's finite completeness Theorem [35]
