Résumé
We view the vectors of a distributional semantic model as vectors of a semi-module over the semi-ring of the real interval I = [0, 1]. We show that the quantum logic of projectors is distributive and includes a Boolean sublattice. The compositional functional semantics of pregroup grammars interprets words and sentences as vectors such that the first order formula, the pregroup vector and the semantic vector interpreting a sentence are equivalent.