# Relational Causal Models with Cycles:Representation and Reasoning

arXiv: https://arxiv.org/abs/2202.10706 · HTML: https://mlsanity.com/paper/2202.10706/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Causal reasoning in LLMs, one of 17 directions in LLM reasoning.
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Placed in

- LLM reasoning / [Causal reasoning in LLMs](https://mlsanity.com/lr/causal-reasoning-in-llms/)

## Builds on (most cited first, 11 of 11)

- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [Markov Properties for Graphical Models with Cycles and Latent Variables](https://mlsanity.com/paper/1710.08775/) (2017)
- [Directed Cyclic Graphical Representations of Feedback Models](https://mlsanity.com/paper/1302.4982/) (2013)
- [Causal Inference Under Interference And Network Uncertainty](https://mlsanity.com/paper/1907.00221/) (2019)
- [Causal Diagrams for Interference](https://mlsanity.com/paper/1403.1239/) (2014)
- [A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Bias](https://mlsanity.com/paper/1805.02087/) (2018)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Causal inference, social networks, and chain graphs](https://mlsanity.com/paper/1812.04990/) (2018)
- [Towards Robust Relational Causal Discovery](https://mlsanity.com/paper/1912.02390/) (2019)
- [Lifted Representation of Relational Causal Models Revisited: Implications for Reasoning and Structure Learning](https://mlsanity.com/paper/1508.02103/) (2015)
- [Reasoning about Independence in Probabilistic Models of Relational Data](https://mlsanity.com/paper/1302.4381/) (2013)

## Built on by (most cited first, 4 of 4)

- [Lifted Causal Inference in Relational Domains](https://mlsanity.com/paper/2403.10184/) (2024)
- [Learning Relational Causal Models with Cycles through Relational Acyclification](https://mlsanity.com/paper/2208.12210/) (2022)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [Lifted Causal Inference](https://mlsanity.com/paper/2606.28024/) (2026)

## Abstract (arXiv)

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 σ-separation, a new criterion for understanding relational systems with feedback loops. We also introduce a new lifted representation, σ-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 σ-AGG and that relational σ-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.