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Closed categories and categorial grammar. (English) Zbl 0789.03027
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.)
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