Ascertaining Mathematical Theorems
Ascertaining Mathematical Theorems
复制标题
确定数学定理
DOI：
10.1016/j.entcs.2005.11.021
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Patrick F. Smith
中科院分区：
文献类型：
--
作者：
R. McCasland;A. Bundy;Patrick F. Smith
对于大多数逻辑学家来说，“定理”一词指的是任何已被证明为正确的陈述，而对于数学家来说，相对而言，“定理”一词很少被应用，并且表示一些更特殊的东西。在本文中，我们研究了这种术语差异背后的一些根本原因，并展示了如何利用这种差异，以构建一个计算机系统，自动从前者中选择后者类型的“定理”。事实上，我们已经开始构建自动发现系统 MATHsAiD，其设计基于我们的研究。我们提供了该系统产生的一些初步结果，并将这些结果与各种数学教科书中出现的定理进行比较。
Whereas to most logicians, the word “theorem” refers to any statement which has been shown to be true, to mathematicians, the word “Theorem” is, relatively speaking, rarely applied, and denotes something far more special. In this paper, we examine some of the underlying reasons behind this difference in terminology, and we show how this discrepancy might be exploited, in order to build a computer system which automatically selects the latter type of “Theorems” from amongst the former. Indeed, we have begun building the automated discovery system MATHsAiD, the design of which is based upon our research. We provide some preliminary results produced by this system, and compare these results to Theorems appearing in various mathematics textbooks.