多数有向图
Majority Digraphs
摘要：
择多有向图是有限简单有向图$G=(V,\to)$，使得对于顶点$v\in V$存在有限集合$A_v$，并且具有以下性质：$u\to v$当且仅当“超过一半的$A_u$是$A_v$“。也就是说，$u\to v$当且仅当$ |A_u \cap A_v | > \frac{1}{2} \cdot |A_u|$。我们将多数有向图刻画为具有每个有向圈都有反转的性质的有向图。如果我们把$\frac{1}{2}$变换为任意实数$α\in (0,1)$，我们得到了同样类的有向图。我们应用这个刻画结果得到了关于断言逻辑“大多数$X$是$Y$“和命题逻辑标准连接词的一个结果。
英文摘要：
A majority digraph is a finite simple digraph $G=(V,\to)$ such that there exist finite sets $A_v$ for the vertices $v\in V$ with the following property: $u\to v$ if and only if "more than half of the $A_u$ are $A_v$". That is, $u\to v$ if and only if $ |A_u \cap A_v | > \frac{1}{2} \cdot |A_u|$. We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change $\frac{1}{2}$ to any real number $α\in (0,1)$, we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions "most $X$ are $Y$" and the standard connectives of propositional logic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
