| 对角化原理的逻辑形式及其应用 |
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| 引用本文： | 周云才,李克清. 对角化原理的逻辑形式及其应用[J]. 长江大学学报, 2006, 3(1): 11-12 |
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| 作者姓名： | 周云才 李克清 |
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| 作者单位： | 长江大学计算机科学学院,湖北,荆州,434023;长江大学计算机科学学院,湖北,荆州,434023 |
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| 摘 要： | 对角化原理在整个计算科学特别是数学逻辑基础论证中起着至关重要的作用。伯特纳德·罗素用它提出了著名的"理发师悖论",对整个数学的逻辑基础提出了质疑;康托应用它建立了集合的势的理论,其中最著名的一个结论是:不存在最大势的集合;图灵应用它证明了计算理论中著名的"停机问题"。分析了对角化原理的逻辑形式,在比较理发师悖论、Cantor 集合理论和停机问题的思维模式的基础上,研究了其对基础数学学科理论以及计算理论的深刻影响。
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| 关 键 词： | 对角化原理 逻辑形式 理发师悖论 集合 停机问题 |
| 文章编号： | 1673-1409（2006）01-0010-02 |
| 收稿时间： | 2005-11-15 |
| 修稿时间： | 2005-11-15 |
On the Diagonalization Principle and It's Application |
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| ZHOU Yun-cai,LI Ke-qing. On the Diagonalization Principle and It's Application[J]. Journal of Yangtze University, 2006, 3(1): 11-12 |
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| Authors: | ZHOU Yun-cai LI Ke-qing |
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| Abstract: | The diagonalization principle plays an essential role in the whole science of computation,es- pecially in the demonstration of the foundation of math logics.The famous paradox named as"barber paradox"proposed by Bertnard Rullsell questions to the entire foundation of math logics. Cantor es- tablished a theory of cardinals of sets,in which there is the most well-known conclusion,that is there is no max-cardinal.Turing applied it to prove the famous"halting problem"in the computation theo- ry. On the base of comparison of"barber paradox",Cantor's theory of set and"halting problem", the logic form of the diagonalization principle,and it's profound influence on the theory of the basic math- ematic discipline as well as on the computation theory are studied. |
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| Keywords: | the diagonalization principle logic form barber paradox set halting problem |
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