I introduce a novel and quite intuitive interpretation of the ternary relation that figures in the relational semantics of many relevance logics. Conceptually, my interpretation makes use only of incompatibility and parthood relations, defined over a set of states. In this way, the proposed interpretation—of the ternary relation and the conditional—extends Dunn’s and Restall’s works on negation and the Routley star operator. Therefore, the interpretation is unified, and hence not only intuitive but also parsimonious. Additionally, the interpretation provides us with a cogent argument to the effect that a ternary relation is indispensable, and we cannot merely do with a binary relation.

中文翻译：

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关联逻辑语义的统一解释

我介绍了一种新颖且非常直观的对三元关系的解释，这种关系在许多相关逻辑的关系语义学中都有体现。从概念上讲，我的解释仅使用了在一组状态上定义的不相容性和部分关系。通过这种方式，所提出的对三元关系和条件关系的解释扩展了邓恩和雷斯托尔关于否定和 Routley 星算子的工作。因此，解释是统一的，因此不仅直观而且简约。此外，解释为我们提供了一个有说服力的论据，即三元关系是必不可少的，我们不能只用二元关系。