mlsanityData to 7 Oct 2026

Relational Causal Models with Cycles:Representation and Reasoning

arXiv 2202.10706 ↗First posted 22 Feb 2022cs.AI cs.SIcited by 4

On the map: LLM reasoning → Causal reasoning in LLMs

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.

Key facts. Cited by 4 papers in the map (data through 7 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.

Builds on

11 of 33 references.

References · 11

  1. 2013A Discovery Algorithm for Directed Cyclic Graphscited by 33
  2. 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
  3. 2013Directed Cyclic Graphical Representations of Feedback Modelscited by 27
  4. 2019Causal Inference Under Interference And Network Uncertaintycited by 27
  5. 2014Causal Diagrams for Interferencecited by 18
  6. 2018A Constraint-Based Algorithm For Causal Discovery with Cycles, Latent Variables and Selection Biascited by 15
  7. 2013A Sound and Complete Algorithm for Learning Causal Models from Relational Datacited by 12
  8. 2018Causal inference, social networks, and chain graphscited by 11
  9. 2019Towards Robust Relational Causal Discoverycited by 8
  10. 2015Lifted Representation of Relational Causal Models Revisited: Implications for Reasoning and Structure Learningcited by 5
  11. 2013Reasoning about Independence in Probabilistic Models of Relational Datacited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 0; 2026: 1.

4 papers.

  1. 2024Lifted Causal Inference in Relational Domainscited by 7
  2. 2022Learning Relational Causal Models with Cycles through Relational Acyclificationcited by 6
  3. 2023A Survey of Methods, Challenges and Perspectives in Causalitycited by 6
  4. 2026Lifted Causal Inferencecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022Markov categories, causal theories, and the do-calculus
  2. 2023Causal models in string diagrams
  3. 2026Causal Reasoning with Bipartite Graphical Causal Models
  4. 2025Relaxing partition admissibility in Cluster-DAGs: a causal calculus with arbitrary variable clustering
  5. 2025Temporal Causal Reasoning with (Non-Recursive) Structural Equation Models
  6. 2025KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?
  7. 2026Continual learning and refinement of causal models through dynamic predicate invention
  8. 2024CausalGraph2LLM: Evaluating LLMs for Causal Queries