mlsanityData to 14 Oct 2026

Causal Sufficiency and Actual Causation

arXiv 2102.02311 ↗First posted 3 Feb 2021cs.AIcited by 29

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Abstract (arXiv)

Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X=x causes Y=y iff X=x is a Necessary Element of a Sufficient Set for Y=y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are due to Halpern & Pearl. Yet all of them ignore Pearl's first strategy, and the second strategy taken by itself is unable to deliver a consensus. This paper offers a way out by going back to the first strategy: it offers six formal definitions of causal sufficiency and two interpretations of necessity. Combining the two gives twelve new definitions of actual causation. Several interesting results about these definitions and their relation to the various Halpern & Pearl definitions are presented. Afterwards the second strategy is evaluated as well. In order to maximize neutrality, the paper relies mostly on the examples and intuitions of Halpern & Pearl. One definition comes out as being superior to all others, and is therefore suggested as a new definition of actual causation.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 2 of its 27 references that are in the map. First posted on arXiv 3 Feb 2021.

Builds on

2 of 27 references.

References · 2

  1. 2015A Modification of the Halpern-Pearl Definition of Causalitycited by 47
  2. 2020The Counterfactual NESS Definition of Causationcited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 5; 2024: 9; 2025: 7; 2026: 3.

29 papers.

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  1. 2021Local Explanations via Necessity and Sufficiency: Unifying Theory and Practicecited by 45
  2. 2022Causal Explanations and XAIcited by 30
  3. 2022A Causal Analysis of Harmcited by 15
  4. 2022CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking Causal Discovery methodscited by 10
  5. 2022Quantifying Harmcited by 10
  6. 2024Causal Explanations for Image Classifierscited by 9
  7. 2023A Measure-Theoretic Axiomatisation of Causalitycited by 8
  8. 2024Explaining Image Classifierscited by 7
  9. 2025Null Counterfactual Factor Interactions for Goal-Conditioned Reinforcement Learningcited by 6
  10. 2025Rethinking Spatio-Temporal Anomaly Detection: A Vision for Causality-Driven Cybersecuritycited by 6
  11. 2023Multiple Different Black Box Explanations for Image Classifierscited by 4
  12. 2024Automated Discovery of Functional Actual Causes in Complex Environmentscited by 4
17 more
  1. 2025Sufficient, Necessary and Complete Causal Explanations in Image Classificationcited by 4
  2. 2024Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 3
  3. 2023Moral Responsibility for AI Systemscited by 2
  4. 2024Nondeterministic Causal Modelscited by 2
  5. 2024Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 2
  6. 2023Mathematical Explanationscited by 1
  7. 2024Algorithmic Identification of Essential Exogenous Nodes for Causal Sufficiency in Brain Networkscited by 1
  8. 2025Searching for Actual Causes: Approximate Algorithms with Adjustable Precisioncited by 1
  9. 2026Rethinking Chronological Causal Discovery with Signal Processingcited by 1
  10. 2023Integrating Temporality and Causality into Acyclic Argumentation Frameworks using a Transition Systemcited by 0
  11. 2024A Dynamical View of the Question of Whycited by 0
  12. 2024Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisonscited by 0
  13. 2025Actual Causation and Nondeterministic Causal Modelscited by 0
  14. 2025Evaluation of Black-Box XAI Approaches for Predictors of Values of Boolean Formulaecited by 0
  15. 2025Activation-Deactivation: A General Framework for Robust Post-hoc Explainable AIcited by 0
  16. 2026Formalizing and falsifying causal pathways of rare eventscited by 0
  17. 2026Difference-Making without Making a Differencecited by 0