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Alison Pease
Dundee University
  1. 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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    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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    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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  4. 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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    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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    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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  7. 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.