Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.

中文翻译：

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公理之间的理论

中间性作为三个独立点之间的关系已在几何学中得到了广泛研究，并由不同作者在不同背景下公理化。本文提出了一种更为普遍的中间性概念，即三点之间的关系。主要的技术成果是一个完善而完整的逻辑系统，描述了图的顶点集之间这种关系的普遍性质。