nLab monad (in linguistics)

Idea

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:

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.

Related concepts

• monad (in computer science)
• dependent type theoretic methods in natural language semantics

References

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. $\langle M, \eta, \star \rangle$ 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)