  This paper presents and extends our type theoretical framework for a
compositional treatment of natural language semantics with some lexical
features like coercions (e.g. of a town into a football club) and copredication
(e.g. on a town as a set of people and as a location). The second order typed
lambda calculus was shown to be a good framework, and here we discuss how to
introduced predefined types and coercive subtyping which are much more natural
than internally coded similar constructs. Linguistic applications of these new
features are also exemplified.
