The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typical perspectives in causality theory, our equivalence opens the door to more compact and computational proofing techniques, because the language of binary relations is well adapted to equational reasoning. Additionally, and of independent interest, the proofs of the results presented in this paper are checked with the Coq proof assistant.

翻译：d-分离概念在因果理论中占据核心地位，是从因果图中推导条件独立性质的基础工具。Pearl定义了在给定第三个子集的条件下，两个子集之间的d-分离关系。本研究提出一种全新视角：i) 揭示了d-分离如何从非循环图（可能无限）扩展得到；ii) 论证了该概念如何被表述并刻画为顶点间的二元关系。与因果理论中的传统视角相比，我们的等价性为更紧凑的证明计算技术开辟了道路——因为二元关系语言天然适配等式推理。此外，作为独立价值，本文所有结论的证明均已通过Coq证明辅助器验证。