On the notion of interestingness in automated mathematical discovery
On the notion of interestingness in automated mathematical discovery
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DOI：
10.1006/ijhc.2000.0394
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发表时间：
2000-09-01
影响因子：
5.4
通讯作者：
Walsh, T
中科院分区：
文献类型：
--
作者：
Colton, S;Bundy, A;Walsh, T
我们调查了五个数学发现程序，通过详细研究它们所说明的发现过程和它们所取得的成功。我们专注于他们如何估计的概念和图形的兴趣，并提取一些常见的概念，自动数学发现的兴趣。我们详细介绍了经验证据是如何被用来给合理性的预测，以及不同的方式，其中一个结果可以被认为是新颖的。我们还着眼于程序评估的方式如何令人惊讶和复杂的猜想陈述，以及使用概念或猜想的适用性的不同方式。最后，我们注意到用户如何为程序设置任务，以及这如何影响兴趣度的计算。我们的结论与使用有趣的措施，为未来的开发人员发现程序在数学上的一些提示。(C)北京大学出版社.
We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery. We detail how empirical evidence is used to give plausibility to conjectures, and the different ways in which a result can be thought of as novel. We also look at the ways in which the programs assess how surprising and complex a conjecture statement is, and the different ways in which the applicability of a concept or conjecture is used. Finally, we note how a user can set tasks for the program to achieve and how this affects the calculation of interestingness. We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics. (C) 2000 Academic Press.