Closed categories and categorical grammar.
Daniel J. Dougherty · Notre Dame Journal of Formal Logic · 1992
Inspired byLambek's work on categorial grammar, we examine the proposal that the theory of biclosed monoidal categories can serve as a foundation for a formal theory of natural language.The emphasis throughout is on the derivation of the axioms for these categories from linguistic intuitions.When Montague's principle that there is a homomorphism between syntax and semantics is refined to the principle that meaning is a functor between a syntax-category and a semantics-category, the fundamental properties of biclosed categories induce a rudimentary computationally oriented theory of language.• Types are considered as syntactic entities, eligible for semantic interpretation.This allows a model-theoretic analysis of type shifting.• The general character of the theory is computational and algebraic, rather than set-theoretic.• The goal is not an explication of what meanings are, but rather, how they behave.Our paper attempts to show how one might discover categories for language by working from semantic intuitions, and further motivates the approach on methodological grounds (see the discussion of "model-theoretic semantics" be-