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 coercion, next to a rich
nominal lexical semantic structure called qualia structure.
In a previous paper we introduced coercion into the framework of
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 metonymy.
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