The Categorial Fine-Structure of Natural Language
Johan van Benthem

Abstract:
Categorial grammar analyzes linguistic syntax and semantics in terms
of type theory and lambda calculus. A major attraction of this
approach is its unifying power, as its basic function/argument
structures occur across the foundations of mathematics, language and
computation. This paper considers, in a light example-based manner,
where this elegant logical paradigm stands when confronted with the
wear and tear of reality. Starting from a brief history of the Lambek
tradition since the 1980s, we discuss three main issues: (a) the fit
of the lambda calculus engine to characteristic semantic structures in
natural language, (b) the coexistence of the original type-theoretic
and more recent modal interpretations of categorial logics, and (c)
the place of categorial grammars in the complex total architecture of
natural language, which involves - amongst others - mixtures of
interpretation and inference.