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