Linguistics is the (scientific) study of natural human language. See a reasonably good page at Wikipedia.

In mathematics and computer science, we are however also interested in artificial analogues of natural languages: formal and computer? languages.

Formal Linguistics

Linguists often attempt to specify formal grammars (such as context free grammars) which generate exactly the strings of a human language. The derivation trees of such strings are often interpreted in a formal system such as typed lambda calculus, which is taken to represent a high level description of the meaning the speaker intends. Such a “semantics” should ideally assign meanings to the smallest meaningful subparts of a sentence such that these submeanings compose to assign meanings to sentences.

Categorial Grammar/Typelogical Grammar

Categorial grammar (Wikipedia) is a tradition in formal syntax which draws inspiration from category theory.

Derivation trees categorify to string diagrams.

A seminal article, inspired by the structure of a (non-symmetric) biclosed monoidal category is:

  • Lambek, J. (1958). The mathematics of sentence structure. American mathematical monthly, 154-170. link

The connection to biclosed monoidal categories is made explicit in:

  • Lambek, J. (1988). Categorial and categorical grammars. In Categorial grammars and natural language structures (pp. 297-317). Springer Netherlands.

Pregroup grammar (Wikipedia) is a refinement of this, and categorifies to (non-symmetric) rigid monoidal categories.

  • Preller, A. (2005). Category theoretical semantics for pregroup grammars. In Logical aspects of computational linguistics (pp. 238-254). Springer Berlin Heidelberg.

  • Preller, A., & Lambek, J. (2007). Free compact 2-categories. Mathematical Structures in Computer Science, 17(2), 309-340.

Revised on August 18, 2014 11:55:10 by Colin Zwanziger (