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  1.  33
    Explanation in Mathematical Conversations: An Empirical Investigation.Alison Pease, Andrew Aberdein & Ursula Martin - 2019 - Philosophical Transactions of the Royal Society A 377.
    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, the other on a random sample of comments lacking (...)
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  2.  37
    The Argument Web: An Online Ecosystem of Tools, Systems and Services for Argumentation.Mark Snaith, Alison Pease, John Lawrence, Barbara Konat, Mathilde Janier, Rory Duthie, Katarzyna Budzynska & Chris Reed - 2017 - Philosophy and Technology 30 (2):137-160.
    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 of domains, languages and activity types. (...)
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  3.  19
    Argumentation Theory for Mathematical Argument.Joseph Corneli, Ursula Martin, Dave Murray-Rust, Gabriela Rino Nesin & Alison Pease - 2019 - Argumentation 33 (2):173-214.
    To adequately model mathematical arguments the analyst must be able to represent the mathematical objects under discussion and the relationships between them, as well as inferences drawn about these objects and relationships as the discourse unfolds. We introduce a framework with these properties, which has been used to analyse mathematical dialogues and expository texts. The framework can recover salient elements of discourse at, and within, the sentence level, as well as the way mathematical content connects to form larger argumentative structures. (...)
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  4. Five Theories of Reasoning: Interconnections and Applications to Mathematics.Alison Pease & Andrew Aberdein - 2011 - Logic and Logical Philosophy 20 (1-2):7-57.
    The last century has seen many disciplines place a greater priority on understanding how people reason in a particular domain, and several illuminating theories of informal logic and argumentation have been developed. Perhaps owing to their diverse backgrounds, there are several connections and overlapping ideas between the theories, which appear to have been overlooked. We focus on Peirce’s development of abductive reasoning [39], Toulmin’s argumentation layout [52], Lakatos’s theory of reasoning in mathematics [23], Pollock’s notions of counterexample [44], and argumentation (...)
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  5.  55
    Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics.Alison Pease, Alan Smaill, Simon Colton & John Lee - 2009 - Foundations of Science 14 (1-2):111-135.
    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 Euler’s conjecture, in which we use work (...)
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  6.  81
    Developments in Research on Mathematical Practice and Cognition.Alison Pease, Markus Guhe & Alan Smaill - 2013 - Topics in Cognitive Science 5 (2):224-230.
    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.
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  7. A Cognitive Model of Discovering Commutativity.Markus Guhe, Alison Pease & Alan Smaill - 2009 - In N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society. pp. 727--732.
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  8. Modelling Serendipity in a Computational Context.Joseph Corneli, Alison Pease, Simon Colton, Anna Jordanous & Christian Guckelsberger - unknown
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  9.  18
    Mathematical Reasoning with Higher-Order Anti-Unifcation.Markus Guhe, Alison Pease, Alan Smaill, Martin Schmidt, Helmar Gust, Kai-Uwe Kühnberger & Ulf Krumnack - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
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  10.  1
    Enabling mathematical cultures: introduction.Benedikt Löwe, Ursula Martin & Alison Pease - forthcoming - Synthese:1-7.
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  11. A Computational Model Of Lakatos-Style Reasoning.Alison Pease - 2013 - Philosophy of Mathematics Education Journal 27.
     
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  12.  9
    Abstract or Not Abstract? Well, It Depends….Alison Pease, Alan Smaill & Markus Guhe - 2009 - Behavioral and Brain Sciences 32 (3-4):345-346.
    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 all-or-nothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested.
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  13. Lakatos-Style Collaborative Mathematics Through Dialectical, Structured and Abstract Argumentation.Alison Pease, John Lawrence, Katarzyna Budzynska, Joseph Corneli & Chris Reed - 2017 - Artificial Intelligence 246:181-219.
  14. Proceedings of AISB 2010 Symposium on Mathematical Practice and Cognition.Alison Pease, Markus Guhe & Alan Smaill (eds.) - 2010 - AISB.
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  15. Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012.Alison Pease & Brendan Larvor (eds.) - 2012 - Society for the Study of Artificial Intelligence and the Simulation of Behaviour.
  16.  7
    Using Crowdsourced Mathematics to Understand Mathematical Practice.Alison Pease, Ursula Martin, Fenner Stanley Tanswell & Andrew Aberdein - 2020 - ZDM 52 (6):1087-1098.
    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 (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of (...)
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  17.  3
    Ethical Challenges in Argumentation and Dialogue in a Healthcare Context.Mark Snaith, Rasmus Øjvind Nielsen, Sita Ramchandra Kotnis & Alison Pease - forthcoming - Argument and Computation:1-16.
    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 dialogue-based e-health systems that provide justified general health advice offers a cost-effective 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 e-health systems, that have a particular relevance to dialogue and argumentation: collecting (...)
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