My colleagues and I use computer algorithms and controlled experiments to model how people speak and write. An example is K. van Deemter (2016), "Computational Models of Referring: A Study in Cognitive Science", MIT Press (now freely downloadable). 

1. Ambiguity and vagueness. I’m interested not only in the strengths of natural languages, but also their potential weaknesses. Sentences in English (Dutch, Chinese, etc.) can often be interpreted in a baffling number of ways, or they can lack precision in other ways. Why is this? Can it sometimes be a strength rather than a weakness?

• Example: Long ago, I edited (with Stanley Peters) a book that helped to focus linguists' and logicians' attention on the phenomena of ambiguity and underspecification.
• Example: Not Exactly: in Praise of Vagueness (OUP 2010) addresses readers both within and outside my field. It discusses how vagueness comes up in communication, how it can be modelled in mathematical logic, and how it can be handled when computers speak or write.
• Example: In this book chapter.pdf (prefinal draft), entitled The Elusive Benefits of Vagueness, Matthew Green and I (2019) investigated when and how it might help a listener to be vague. Our conclusion, after a series of controlled experiments, is that the advantages ascribed to vagueness can often be explained by other factors (e.g., the fact that non-subitizable numbers are processed slowly in spoken language). 
   

2. Referring Expressions Generation. With psychologists and other colleagues, I work on computational models of referring.

• Work by my colleagues and I on this topic started with this article on the generation of logically rich referring expressions (2002), continued with this assessment of some classic algorithms (2012), this survey,  this stochastic model (2019). I explain and contextualise this line of work in my book, Computational Models of Referring: a Study in Cognitive Science.
• Fahime Same and Guanyi Chen have taken the lead on modelling the use of referring expressions in linguistic context. See this paper, for example.
   

3. Logic in Language. We construct algorithms that capture the way logical structures are expressed in human language.

• Example: Explaining Logical Formulas in English. Eduardo Calo's PhD project, which is part of an EU project on Natural Language Technology for Explainable Artificial Intelligence" (NL4XAI), aims to generate clear and succinct textual explanations of formulas of First Order Predicate Logic.
• Example: Models of quantification. In this article, Guanyi Chen and I model how speakers choose combinations of quantified expressions to describe complex visual scenes.
   

4. Cross-linguistic Pragmatics. We use experiments and algorithms to understand the pragmatic mechanisms that govern communication in different languages. Our current focus is on Chinese and English: 

• Guanyi Chen's work on James Huang’s “coolness” hypothesis. This is the well-known but largely unproven hypothesis that the languages of the Far East trade off clarity and brevity differently from those of Europe. To understand in detail what's going on, Guanyi constructs and tests computational models of the phenomena in question. 
   

5. Methodological issues in NLP. I'm keenly interested in the question of what are the strengths and limitations of today's NLP models. For example, how much insight can be gained from LLMs about human language and communication? Examples are my recent papers, Dimensions of Explanatory Value in NLP Models, and The Pitfalls of Defining Hallucination, both published in the journal Computational Linguistics.