We discuss an extension of the standard logical rules (functional application
and abstraction) in Categorial Grammar (CG), in order to deal with some
specific cases of polysemy. We borrow from Generative Lexicon theory which
proposes the mechanism of {\em coercion}, next to a rich nominal lexical
semantic structure called {\em qualia structure}.
In a previous paper we introduced coercion into the framework of {\em
sign-based} Categorial Grammar and investigated its impact on traditional
Fregean compositionality. In this paper we will elaborate on this idea, mostly
working towards the introduction of a new semantic dimension. Where in current
versions of sign-based Categorial Grammar only two representations are derived:
a prosodic one (form) and a logical one (modelling), here we introduce also a
more detaled representation of the lexical semantics. This extra knowledge will
serve to account for linguistic phenomena like {\em metonymy\/}.Comment: LaTeX file, 19 pages, uses pubsmacs, pubsbib, pubsarticle, leqn
