nLab categorial grammar




Categorial grammar is a tradition in formal linguistics which draws inspiration from category theory.

Some History

Syntactic “calculus” for categorial grammars was introduced by Lambek formalizing the function type constructors. Derivation trees can nowadays be encoded by string diagrams.

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

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 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.

A contemporary thesis in this area:

  • Matteo Capelletti, The non-associative Lambek calculus, Logic, Linguistic and Computational Properties, thesis, Bologna, pdf

  • Wikipedia: categorial grammar, combinatory categorial grammar

  • Mati Pentus, Lambek calculus and formal grammars, Amer. Math. Soc. Transl. 1997

  • Michael Moortgat, Categorial type logics, pdf (ch. 2 in Handbook of logic and language, Elsevier 1997)

Research along similar lines is sometimes described as typelogical grammar (See the link below!).


  • Daniel J. Dougherty, Closed Categories and Categorial Grammar , Notre Dame Journal of Formal Logic 34 no.1 (1993) pp.36-49. (pdf)

  • Philippe de Groote, Towards Abstract Categorial Grammars, In: Association for Computational Linguistics, 39th Annual Meeting and 10th Conference of the European Chapter, Proceedings of the Conference, pages 148–155, Toulouse, France, 2001. (pdf)

Last revised on October 9, 2020 at 09:33:08. See the history of this page for a list of all contributions to it.