Categorial Grammar at a Cross-Roads
Johan van Benthem

Abstract:
Categorial grammars are driven by substructural 
logics. These are fragments of modal logics for 
the structures the grammar deals with. We discuss
modal languages as a means of access to families
of relevant structures: formal languages, type
hierarchies, relation algebras c.q. arrow models,
and even geometrical vector spaces.

Keywords: categorial grammar, Lambek Calculus,
ternary models, types, parsing, 
modal logic