In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of graphical models, relational causal models, can represent and reason about complex dynamic systems exhibiting such cycles or feedback loops. Existing cyclic causal discovery algorithms for learning causal models from observational data assume that the data instances are independent and identically distributed which makes them unsuitable for relational causal models. At the same time, causal discovery algorithms for relational causal models assume acyclicity. In this work, we examine the necessary and sufficient conditions under which a constraint-based relational causal discovery algorithm is sound and complete for cyclic relational causal models. We introduce relational acyclification, an operation specifically designed for relational models that enables reasoning about the identifiability of cyclic relational causal models. We show that under the assumptions of relational acyclification and $\sigma$-faithfulness, the relational causal discovery algorithm RCD (Maier et al. 2013) is sound and complete for cyclic models. We present experimental results to support our claim.

翻译：在涉及相互关联单位之间相互影响或因果效应的现实世界现象中,均衡状态通常在图形模型中以循环方式呈现。一个显示式的图形模型类别、关系因果模型,可以代表显示这种循环或反馈循环的复杂动态系统并解释其原因。现有的从观察数据中学习因果模型的循环因果发现算法假设数据实例是独立的,分布相同,因此不适合关系因果模型。与此同时,关系因果模型的因果发现算法假设了周期性。在这项工作中,我们研究了基于约束性因果发现算法对于循环因果模型来说是合理和完整的必要和充分条件。我们采用了关系循环循环循环计算法,这是专门为关系模型设计的一种可解释循环因果关系因果模型的计算方法。我们表明,根据关系循环法的假设和美美美之美-信仰,关系因果解算法(Maier等人,2013年)对于循环模型来说是合理和完整的。我们提出了支持我们主张的实验结果。</s>