
Lakatosstyle collaborative mathematics through dialectical, structured and abstract argumentationArtificial Intelligence 246 181219. 2017.

3Ethical challenges in argumentation and dialogue in a healthcare contextArgument and Computation 116. forthcoming.As the average age of the population increases, so too do the number of people living with chronic illnesses. With limited resources available, the development of dialoguebased ehealth systems that provide justified general health advice offers a costeffective solution to the management of chronic conditions. It is however imperative that such systems are responsible in their approach. We present in this paper two main challenges for the deployment of ehealth systems, that have a particular …Read more

6Using Crowdsourced Mathematics to Understand Mathematical PracticeZDM 52 (6): 10871098. 2020.Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (compar…Read more

29Explanation in mathematical conversations: An empirical investigationPhilosophical Transactions of the Royal Society A 377. 2019.Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, th…Read more

37The Argument Web: an Online Ecosystem of Tools, Systems and Services for ArgumentationPhilosophy and Technology 30 (2): 137160. 2017.The Argument Web is maturing as both a platform built upon a synthesis of many contemporary theories of argumentation in philosophy and also as an ecosystem in which various applications and application components are contributed by different research groups around the world. It already hosts the largest publicly accessible corpora of argumentation and has the largest number of interoperable and cross compatible tools for the analysis, navigation and evaluation of arguments across a broad range …Read more

9Abstract or not abstract? Well, it depends…Behavioral and Brain Sciences 32 (34): 345346. 2009.The target article by Cohen Kadosh & Walsh (CK&W) raises questions as to the precise nature of the notion of abstractness that is intended. We note that there are various uses of the term, and also more generally in mathematics, and suggest that abstractness is not an allornothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested

Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012 (edited book)Society for the Study of Artificial Intelligence and the Simulation of Behaviour. 2012.

9A cognitive model of discovering commutativityIn N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society, . pp. 727732. 2009.

55Bridging the gap between argumentation theory and the philosophy of mathematicsFoundations of Science 14 (12): 111135. 2009.We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Eu…Read more

18Mathematical reasoning with higherorder antiunifcationIn S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society, Cognitive Science Society. 2010.

81Developments in Research on Mathematical Practice and CognitionTopics in Cognitive Science 5 (2): 224230. 2013.We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing

A Computational Model Of Lakatosstyle ReasoningPhilosophy of Mathematics Education Journal 27. 2013.