# Is Causal Reasoning Harder than Probabilistic Reasoning?

arXiv: https://arxiv.org/abs/2111.13936 · HTML: https://mlsanity.com/paper/2111.13936/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2021.

## Built on by (most cited first, 10 of 10)

- [Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions](https://mlsanity.com/paper/2306.14351/) (2023)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [The Hardness of Reasoning about Probabilities and Causality](https://mlsanity.com/paper/2305.09508/) (2023)
- [On Probabilistic and Causal Reasoning with Summation Operators](https://mlsanity.com/paper/2405.03069/) (2024)
- [Modeling Discrimination with Causal Abstraction](https://mlsanity.com/paper/2501.08429/) (2025)
- [Probabilistic Modelling is Sufficient for Causal Inference](https://mlsanity.com/paper/2512.23408/) (2025)
- [Probabilistic and Causal Satisfiability: Constraining the Model](https://mlsanity.com/paper/2504.19944/) (2025)
- [Interleaving Logic and Counting](https://mlsanity.com/paper/2507.05219/) (2025)
- [Gateways to Tractability for Satisfiability in Pearl's Causal Hierarchy](https://mlsanity.com/paper/2511.08091/) (2025)
- [Certifying Interventional Agreement Among Observationally Equivalent Causal Models](https://mlsanity.com/paper/2609.32247/) (2026)

## Abstract (arXiv)

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or "associational") languages. Despite several senses in which causal reasoning is indeed more complex -- both expressively and inferentially -- we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well known probability logics, in particular demonstrating the existsℝ-completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability.