nLab monad (in linguistics)


A number of researchers have proposed that the category theoretic concept of monads may play a role in understanding semantic and pragmatic issues in the use of natural language.

Side effects are to programming languages what pragmatics are to natural languages: they both study how expressions interact with the worlds of their users. It might then come as no surprise that phenomena such as anaphora, presupposition, deixis and conventional implicature yield a monadic description. (Maršík Amblard 2016, p. 3)


In overview papers (Cohn-Gordon, Asudeh), it is proposed that the following topics are explained by specific monads:

  1. Conventional implicature: the writer monad
  2. Optional arguments: the maybe monad
  3. Presupposition failure: the exception monad
  4. Anaphora: the state monad and set monad
  5. Perspective, opacity and intentionality: the reader monad
  6. Conjunction fallacies: the probability monad
  7. Quantifier Scope: the continuation monad
  8. Focus: the pointed set monad
  9. Interrogatives: the set monad
  10. Performatives: the IO monad

In (Burke 1) it is claimed that hyperintensionality can be analysed via monads and applicatives, while in (Burke 2) cross-sentential intensional anaphora is modelled using continuations.


For a summary of uses, see

  • Reuben Cohn-Gordon, Monad Transformers for Natural Language: Combining Monads to Model Effect Interaction, pdf

  • Ash Asudeh, Monads: Some Linguistic Applications, pdf

  • Gianluca Giorgolo and Ash Asudeh, Natural Language Semantics with Enriched Meanings, pdf

These refer to:

  • Gianluca Giorgolo and Ash Asudeh, 2011. Multidimensional Semantics with Unidimensional Glue Logic. In Butt and King 2011, 236–256.
  • Gianluca Giorgolo and Ash Asudeh, 2012a. M,η,\langle M, \eta, \star \rangle Monads for Conventional Implicatures. In Ana Aguilar Guevara, Anna Chernilovskaya, and Rick Nouwen, eds., Proceedings of Sinn und Bedeutung 16. MIT Working Papers in Linguistics.
  • Gianluca Giorgolo and Ash Asudeh, 2012b. Missing Resources in a Resource-Sensitive Semantics. In Miriam Butt and Tracy Holloway King, eds., Proceedings of the LFG12 Conference, 219–239. Stanford, CA: CSLI Publications.
  • Gianluca Giorgolo and Ash Asudeh, 2013a. Monads as a Solution for Generalized Opacity. Ms., University of Oxford.
  • Gianluca Giorgolo and Ash Asudeh, 2013b. One Semiring to Rule Them All. Ms., University of Oxford.
  • Ash Asudeh and Gianluca Giorgolo, 2016. Perspectives. Semantics and Pragmatics vol. 9, doi.
  • Shan, Chung-chieh. 2001. Monads for Natural Language Semantics. In Kristina Striegnitz, ed., Proceedings of the ESSLLI-2001 Student Session, 285–298. 13th European Summer School in Logic, Language and Information.
  • Christina Unger, 2011. Dynamic Semantics as Monadic Computation. In Manabu Okumura, Daisuke Bekki, and Ken Satoh, eds., New Frontiers in Artificial Intelligence - JSAI-isAI 2011, 68–81.
  • Simon Charlow, 2014. On the semantics of exceptional scope, New York University dissertation.

For work on hypertensionality, see:

  • Luke Burke, Monads for hyperintensionality? A situation semantics for hyperintensional side effects and intra-sentential anaphora, pdf

  • Luke Burke, P-HYPE: A monadic situation semantics for hyperintensional side effects, pdf

For the specific use of continuation-passing style techniques, see

  • Chris Barker, Chung-Chieh Shan, Continuations and Natural Language, OUP, 2014, (introduction)
  • Chris Barker, Continuations and the nature of quantification, Natural Language Semantics, 10(3):211–242, 2002.
  • Chris Barker, Continuations in natural language, in Hayo Thielecke, editor, Proceedings of the Fourth ACM SIGPLAN Continuations Workshop (CW’04), Birmingham, UK, 2004.
  • Ekaterina Lebedeva, Expression de la dynamique du discours à l’aide de continuations, (thesis)

The alternative approach to treating side effects, known as algebraic effects, has also been employed in natural language semantics:

  • Jirka Maršík, Maxime Amblard, Algebraic Effects and Handlers in Natural Language Interpretation, pdf
  • Jirka Maršík, Maxime Amblard, Introducing a Calculus of Effects and Handlers for Natural Language Semantics, arXiv:1606.06125

The weaker notion of applicative functors has also been used:

  • Oleg Kiselyov, Applicative Abstract Categorial Grammars, (pdf)
  • Oleg Kiselyov, Applicative Abstract Categorial Grammars in Full Swing, (pdf)
  • Simon Charlow, A modular theory of pronouns and binding, (pdf)

Last revised on October 13, 2023 at 10:31:20. See the history of this page for a list of all contributions to it.