The Role of Structural Reasoning in the Genesis of Graph Theory
The Role of Structural Reasoning in the Genesis of Graph Theory
复制标题
结构推理在图论起源中的作用
DOI：
10.1080/01445340.2019.1608493
复制
发表时间：
2019
影响因子：
0.5
通讯作者：
中科院分区：
文献类型：
--
作者：
dsamnes Kőnig在1936年出版的关于图论的开创性著作，收集了汉密尔顿、凯利、西尔维斯特等人在19世纪中后期的先驱著作中的概念和结果。更重要的是，Kőnig自己贡献了许多他在二十多年来一直致力于这个主题的研究中获得的成果。值得注意的是，他所谓的有向图的基本原理几乎全部来自保罗·赫兹1922年关于这种形式的句子的结构推理的文章。尽管Kőnig在他的书中充分承认了这一点，但这在逻辑圈中并不是众所周知的事实。考虑到近几十年来用图来描述和解释逻辑问题的众多趋势，赫兹的结构推理基础首先为图论的基本概念提供了信息，这一事实非常重要。本文的主要目标是总结赫兹的文章，并展示Kőnig如何整合他的书中提出的概念和结果。接下来是赫兹的结果如何以及何时在图论方面被重新发明的阐述。赫兹和Kőnig都认为赫兹在1923年的一篇同伴文章中引入的这种形式的更一般的句子不能用图来解释，对这种观点进行了批判性的讨论，从而结束了本文。
The seminal book on graph theory by Dénes Kőnig, published in the year 1936, collected notions and results from precursory works from the mid to late nineteenth century by Hamilton, Cayley, Sylvester and others. More importantly, Kőnig himself contributed many of his own results that he had obtained in the more than twenty years that he had been working on this subject matter. What is noteworthy is the fact that the fundamentals of what he callsdirectedgraphs are taken almost exhaustively from Paul Hertz' 1922 article on structural reasoning about sentences of the form. This is not a fact that is well known in logical circles, even though Kőnig fully acknowledges this in his book. In view of the numerous trends in the recent decades to describe and explicate logical matters by means of graphs, the fact that it was Hertz' foundation of structural reasoning that informed basic notions of graph theory in the first place is highly significant. The main goal of this paper is to summarize Hertz' article and demonstrate how Kőnig integrates the notions and results presented therein in his book. This is followed by an exposition of how and when Hertz' results were reinvented in terms of graph theory. A critical discussion of the opinion expressed by both Hertz and Kőnig that the more general sentences of the form, introduced by Hertz in a companion article in 1923, cannot be interpreted by graphs concludes this paper.
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DOI：
10.1007/978-1-4684-8971-2_2
发表时间：
1990
期刊：
--
影响因子：
--
作者：
D. König
通讯作者：
D. König
影响因子：
1.4
作者：
P. Hertz;J. Legris
通讯作者：
J. Legris
ber Axiomensysteme fr beliebige Satzsysteme：Teil II。
影响因子：
1.4
作者：
P. Hertz
通讯作者：
P. Hertz
影响因子：
0.9
作者：
P. Hertz
通讯作者：
P. Hertz
Gentzen 的证明系统：天才作品的副产品
DOI：
10.2178/bsl/1344861886
发表时间：
2012
期刊：
Bull. Symb. Log.
影响因子：
--
作者：
J. Plato
通讯作者：
J. Plato