Dougherty, Daniel J. Closed categories and categorial grammar. (English) Zbl 0789.03027 Notre Dame J. Formal Logic 34, No. 1, 36-49 (1993). Summary: 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. MSC: 03B65 Logic of natural languages 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) Keywords:categorial grammar; biclosed monoidal categories; formal theory of natural language PDF BibTeX XML Cite \textit{D. J. Dougherty}, Notre Dame J. Formal Logic 34, No. 1, 36--49 (1993; Zbl 0789.03027) Full Text: DOI