门格尔定理的形式化方法

Reports Math. Log. Pub Date : 2022-11-28 DOI:10.4467/20842589rm.22.003.16660

Roberta Bonacina, Daniel Misselbeck-Wessel

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引用次数: 0

摘要

门格尔图定理将非相邻顶点a和b的分离集的最小大小等同于a和b之间不相交路径的最大数量。通过捕获分离集作为蕴涵关系的模型，我们采用了门格尔结果的形式化方法。在证明不一致性是以存在足够多的不相交路径为特征的基础上，我们用完备性的方法恢复了门格尔定理。

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A formal approach to Menger's theorem

Menger's graph theorem equates the minimum size of a separating set for non-adjacent vertices a and b with the maximum number of disjoint paths between a and b. By capturing separating sets as models of an entailment relation, we take a formal approach to Menger's result. Upon showing that inconsistency is characterised by the existence of suficiently many disjoint paths, we recover Menger's theorem by way of completeness.

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Reports Math. Log.

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