  We present a framework, named the Montagovian generative lexicon, for
computing the semantics of natural language sentences, expressed in many sorted
higher order logic. Word meaning is depicted by lambda terms of second order
lambda calculus (Girard's system F) with base types including a type for
propositions and many types for sorts of a many sorted logic. This framework is
able to integrate a proper treatment of lexical phenomena into a Montagovian
compositional semantics, including the restriction of selection which imposes
the nature of the arguments of a predicate, and the possible adaptation of a
word meaning to some contexts. Among these adaptations of a word's sense to the
context, ontological inclusions are handled by an extension of system F with
coercive subtyping that is introduced in the present paper. The benefits of
this framework for lexical pragmatics are illustrated on meaning transfers and
coercions, on possible and impossible copredication over different senses, on
deverbal ambiguities, and on "fictive motion". Next we show that the
compositional treatment of determiners, quantifiers, plurals,... are finer
grained in our framework. We then conclude with the linguistic, logical and
computational perspectives opened by the Montagovian generative lexicon.
