Montague Semantics for Lambek Pregroups

Lambek pregroups are algebraic structures modelling natural language syntax, while Montague captures semantics as a homomorphism from syntax to first-order logic. We introduce the variant RelCoCat of the categorical compositional distributional (DisCoCat) models of Coecke et al. where linear maps are replaced by relations. Our main result is a factorisation of RelCoCat models through free cartesian bicategories, as a corollary we get a logspace reduction from the semantics problem to the evaluation of conjunctive queries. Finally, we define question answering as an NP-complete problem.