Using Analogical Representations for Mathematical Concept Formation

机译：使用类比表示法进行数学概念形成

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We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of "visual" concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.

机译：我们认为，自动概念形成系统可以使用数学概念的可视化表示来发展数学中的其他概念和猜想。我们考虑了视觉推理在人类数学发展中的作用，并考虑了数学与视觉之间关系的某些方面，包括以数学为创作灵感的艺术家（然后可能会反馈到数学发展中），评估数学的视觉美感，视觉上令人愉悦的数学以及使用视觉发展数学概念的方式。我们以“视觉”概念和猜想为例，激发数字类型的类比表示，并提出一个自动化案例研究，在该案例中，我们使自动化的理论形成程序能够读取这种类型的视觉类比表示。

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《Model-based reasoning in science and technology : Abduction, logic, and computational discovery》|2009年|p.301-314|共14页
会议地点 Campinas(BR);Campinas(BR)
作者
Alison Pease; Simon Colton; Ramin Ramezani; Alan Smaill; Markus Guhe;
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作者单位

School of Informatics, University of Edinburgh, Informatics Forum,10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom;

rnDepartment of Computing, Imperial College London, 180 Queens Gate,London, SW7 2RH, United Kingdom;

rnDepartment of Computing, Imperial College London, 180 Queens Gate,London, SW7 2RH, United Kingdom;

rnSchool of Informatics, University of Edinburgh, Informatics Forum,10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom;

rnSchool of Informatics, University of Edinburgh, Informatics Forum,10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom;

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原文格式 PDF
正文语种 eng
中图分类自动推理、机器学习;
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Using Analogical Representations for Mathematical Concept Formation

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