mlsanityData to 7 Oct 2026

Probabilistic Reasoning across the Causal Hierarchy

arXiv 2001.02889 ↗First posted 9 Jan 2020cs.LO cs.AIcited by 19

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Abstract (arXiv)

We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning -- including conditional independence and Bayesian inference -- the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jan 2020.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 4; 2024: 4; 2025: 6; 2026: 1.

19 papers.

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  1. 2022Neural Causal Models for Counterfactual Identification and Estimationcited by 54
  2. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  3. 2023Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractionscited by 11
  4. 2021A Topological Perspective on Causal Inferencecited by 10
  5. 2023A Measure-Theoretic Axiomatisation of Causalitycited by 8
  6. 2024Learning Structural Causal Models through Deep Generative Models: Methods, Guarantees, and Challengescited by 8
  7. 2025What is causal about causal models and representations?cited by 6
  8. 2025Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoptioncited by 6
  9. 2023The Hardness of Reasoning about Probabilities and Causalitycited by 4
  10. 2022Formalizing Statistical Causality via Modal Logiccited by 2
  11. 2024On Probabilistic and Causal Reasoning with Summation Operatorscited by 2
  12. 2024Nondeterministic Causal Modelscited by 2
7 more
  1. 2025Probabilistic Modelling is Sufficient for Causal Inferencecited by 2
  2. 2021Observing Interventions: A logic for thinking about experimentscited by 1
  3. 2025Probabilistic and Causal Satisfiability: Constraining the Modelcited by 1
  4. 2024Teleporter Theory: A General and Simple Approach for Modeling Cross-World Counterfactual Causalitycited by 0
  5. 2025Learning Counterfactual Outcomes Under Rank Preservationcited by 0
  6. 2025Gateways to Tractability for Satisfiability in Pearl's Causal Hierarchycited by 0
  7. 2026Certifying Interventional Agreement Among Observationally Equivalent Causal Modelscited by 0