In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the past years. In particular, we consider the transitivity properties corresponding to the six relational compositions of ternary relations recently introduced by Bakri et al., making a careful distinction between the four associative ones and the two non-associative ones.

中文翻译：

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三元关系的封闭与开放

在本文中，我们研究了关于各种关系属性的三元关系的关闭或打开问题，重点是过去几年为三元关系提出的许多传递性属性。特别是，我们考虑了与 Bakri 等人最近引入的三元关系的六种关系组合相对应的传递性属性，仔细区分了四种关联的和两种非关联的。