Causal reasoning in relational domains is fundamental to studying real-world
social phenomena in which individual units can influence each other's traits
and behavior. Dynamics between interconnected units can be represented as an
instantiation of a relational causal model; however, causal reasoning over such
instantiation requires additional templating assumptions that capture feedback
loops of influence. Previous research has developed lifted representations to
address the relational nature of such dynamics but has strictly required that
the representation has no cycles. To facilitate cycles in relational
representation and learning, we introduce relational $\sigma$-separation, a new
criterion for understanding relational systems with feedback loops. We also
introduce a new lifted representation, $\sigma$-abstract ground graph which
helps with abstracting statistical independence relations in all possible
instantiations of the cyclic relational model. We show the necessary and
sufficient conditions for the completeness of $\sigma$-AGG and that relational
$\sigma$-separation is sound and complete in the presence of one or more cycles
with arbitrary length. To the best of our knowledge, this is the first work on
representation of and reasoning with cyclic relational causal models.

本文介绍了一种新的关于环形关系因果模型的表示方法和推理方法。通过引入关系 σ 分离的新标准，以及一种新的提升表示，σ- 抽象地面图，帮助在所有可能的实例化中抽象统计独立关系。我们还表明，基于 σ-AGG，关系 σ 分离对于任意长度的一个或多个循环的存在是完整的和有必要的。本文是有关现有研究所建立的第一个运行时表示和推理循环关系因果模型。