Closed Categories and Categorial Grammar. Dougherty, D. J.\ Notre Dame Journal of Formal Logic, 34(1):36--49, 1993.
Paper abstract bibtex Inspired by Lambek'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.
@article{ a_ndjfl93,
title = {Closed Categories and Categorial Grammar},
author = {Daniel J.\ Dougherty},
pages = {36--49},
journal = {Notre Dame Journal of Formal Logic},
year = {1993},
volume = {34},
number = {1},
abstract = {Inspired by Lambek'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. },
url = {ndjfl93.pdf}
}