# A Modification of the Halpern-Pearl Definition of Causality

arXiv: https://arxiv.org/abs/1505.00162 · HTML: https://mlsanity.com/paper/1505.00162/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2015.

## Built on by (most cited first, 30 of 47)

- [Causal Sufficiency and Actual Causation](https://mlsanity.com/paper/2102.02311/) (2021)
- [Counterfactual harm](https://mlsanity.com/paper/2204.12993/) (2022)
- [LLMs Are Prone to Fallacies in Causal Inference](https://mlsanity.com/paper/2406.12158/) (2024)
- [A Causal Analysis of Harm](https://mlsanity.com/paper/2210.05327/) (2022)
- [Explanations for Occluded Images](https://mlsanity.com/paper/2103.03622/) (2021)
- [Quantifying Harm](https://mlsanity.com/paper/2209.15111/) (2022)
- [Answer-Set Programs for Reasoning about Counterfactual Interventions and Responsibility Scores for Classification](https://mlsanity.com/paper/2107.10159/) (2021)
- [Causal Explanations for Image Classifiers](https://mlsanity.com/paper/2411.08875/) (2024)
- [Detecting Multi-Sensor Fusion Errors in Advanced Driver-Assistance Systems](https://mlsanity.com/paper/2109.06404/) (2021)
- [Actual Causality and Responsibility Attribution in Decentralized Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2204.00302/) (2022)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Causal Modeling With Infinitely Many Variables](https://mlsanity.com/paper/2112.09171/) (2021)
- [Occlusion Sensitivity Analysis with Augmentation Subspace Perturbation in Deep Feature Space](https://mlsanity.com/paper/2311.15022/) (2023)
- [Causality from Bottom to Top: A Survey](https://mlsanity.com/paper/2403.11219/) (2024)
- [Anticipating Responsibility in Multiagent Planning](https://mlsanity.com/paper/2307.16685/) (2023)
- [Multiple Different Black Box Explanations for Image Classifiers](https://mlsanity.com/paper/2309.14309/) (2023)
- [Automated Discovery of Functional Actual Causes in Complex Environments](https://mlsanity.com/paper/2404.10883/) (2024)
- [Towards Computationally Efficient Responsibility Attribution in Decentralized Partially Observable MDPs](https://mlsanity.com/paper/2302.12676/) (2023)
- [From Database Repairs to Causality in Databases and Beyond](https://mlsanity.com/paper/2306.09374/) (2023)
- [Score-Based Explanations in Data Management and Machine Learning: An Answer-Set Programming Approach to Counterfactual Analysis](https://mlsanity.com/paper/2106.10562/) (2021)
- [Causal Explanations for Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2205.15462/) (2022)
- [Formalizing Statistical Causality via Modal Logic](https://mlsanity.com/paper/2210.16751/) (2022)
- [Attribution-Scores in Data Management and Explainable Machine Learning](https://mlsanity.com/paper/2308.00184/) (2023)
- [Security Properties as Nested Causal Statements](https://mlsanity.com/paper/2104.00872/) (2021)
- [Learning Causal Models of Autonomous Agents using Interventions](https://mlsanity.com/paper/2108.09586/) (2021)
- [Improving generalization of machine learning-identified biomarkers with causal modeling: an investigation into immune receptor diagnostics](https://mlsanity.com/paper/2204.09291/) (2022)
- [Moral reinforcement learning using actual causation](https://mlsanity.com/paper/2205.08192/) (2022)
- [Counterfactuals Modulo Temporal Logics](https://mlsanity.com/paper/2306.08916/) (2023)
- [The Causal-Effect Score in Data Management](https://mlsanity.com/paper/2502.02495/) (2025)
- [Causality-Based Scores Alignment in Explainable Data Management](https://mlsanity.com/paper/2503.14469/) (2025)

## Abstract (arXiv)

The original Halpern-Pearl definition of causality [Halpern and Pearl, 2001] was updated in the journal version of the paper [Halpern and Pearl, 2005] to deal with some problems pointed out by Hopkins and Pearl [2003]. Here the definition is modified yet again, in a way that (a) leads to a simpler definition, (b) handles the problems pointed out by Hopkins and Pearl, and many others, (c) gives reasonable answers (that agree with those of the original and updated definition) in the standard problematic examples of causality, and (d) has lower complexity than either the original or updated definitions.