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# Relational Causal Models with Cycles: Representation and Reasoning

*Proceedings of the First Conference on Causal Learning and Reasoning*, PMLR 177:1-18, 2022.

#### Abstract

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, $\sigma$-\textit{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.