Assumptions for actual causality in counterfactual causal spaces

Determine assumptions on how the observational and interventional distributions are related within counterfactual causal spaces that are sufficient to accommodate a rigorous definition of actual causality.

Background

The paper distinguishes general (type) causality from actual (token) causality and reviews prominent SCM-based definitions of actual causality (e.g., Halpern–Pearl and Beckers). The authors argue these rely on strong SCM assumptions, such as synchronizing worlds via shared exogenous variables and coupling observational and interventional distributions through structural equations.

Within the proposed framework of counterfactual causal spaces, the authors emphasize that inferring actual causality from observations is ill-posed without additional assumptions connecting observational and interventional distributions. They therefore defer formalizing actual causality in this framework, highlighting the need to identify suitable assumptions to make such a definition viable.

References

It is beyond the scope of this paper to propose a set of assumptions that would accommodate a definition. We leave it as future work to study assumptions that will facilitate the study of actual causality in counterfactual causal spaces.

— Counterfactual Spaces  (2601.00507 - Park et al., 1 Jan 2026) in Appendix A: Actual causality

Validating world-class assumptions linking observed and unperformed interactions and developing tractable objectives remain open.

— When Do Intrinsic Rewards Lead to Exploration?  (2610.02159 - Viteri et al., 1 Oct 2026) in Section 5, final paragraph of Section 5, "Related work and limits"