We make the case for incorporating a notion of time into causal directed acyclic graphs (DAGs). We demonstrate that nontemporal causal DAGs are ambiguous and obstruct justification of the acyclicity assumption. Assuming that causes precede effects, causal relationships are relative to the time order, and causal DAGs require temporal qualification. We propose a formalization via composite causal variables that refer to quantities at one or multiple time points. We emphasize that the acyclicity assumption requires different justifications depending on whether the time order allows cycles. We conclude by discussing implications for the interpretation and applicability of DAGs as causal models.

翻译：我们论证了将时间概念纳入因果有向无环图（DAGs）的必要性。研究表明，非时间性因果DAG存在歧义，且阻碍了无环性假设的合理性证明。基于原因先于结果的假定，因果关系具有时间顺序相对性，因此因果DAG需要时间限定。我们提出了一种形式化方法，通过复合因果变量（即引用单个或多个时间点的量）实现这一目标。我们强调，无环性假设的合理性证明需根据时间顺序是否允许循环而采取不同论证。最后，我们讨论了这些发现对将DAG解释为因果模型及其适用性的启示。