Causal Counterfactuals Reconsidered

2025-12-14

AI Summary

Pearl’s counterfactual semantics, grounded in structural causal models (SCMs), presupposes causal determinism and explicit response variables—limitations that hinder its applicability to unstructured probabilistic causal models. Method: We propose a novel counterfactual probability semantics for *unstructured probabilistic causal models*, requiring only real-world variables, the Markov condition, and causal completeness—without assuming determinism or designated response variables. Leveraging causal abstraction and establishing rigorous semantic equivalence, we construct, for the first time without extending SCMs, a general counterfactual interpretation framework. Contribution/Results: Our semantics reconciles the ontological disagreement between Pearl and Dawid on counterfactuals and proves semantic equivalence with both major unstructured frameworks—the potential outcomes model and the stochastic consistency model. This extends the scope of counterfactual reasoning beyond structured SCMs and provides a rigorous semantic foundation for unstructured causal modeling.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

I develop a novel semantics for probabilities of counterfactuals that generalizes the standard Pearlian semantics: it applies to probabilistic causal models that cannot be extended into realistic structural causal models and are therefore beyond the scope of Pearl's semantics. This generalization is needed because, as I show, such probabilistic causal models arise even in simple settings. My semantics offer a natural compromize in the long-standing debate between Pearl and Dawid over counterfactuals: I agree with Dawid that universal causal determinism and unrealistic variables should be rejected, but I agree with Pearl that a general semantics of counterfactuals is nonetheless possible. I restrict attention to causal models that satisfy the Markov condition, only contain realistic variables, and are causally complete. Although I formulate my proposal using structural causal models, as does Pearl, I refrain from using so-called response variables. Moreover, I prove that my semantics is equivalent to two other recent proposals that do not involve structural causal models, and that it is in line with various comments on stochastic counterfactuals that have appeared in the literature more broadly. Throughout I also reflect on the universality of the Markov condition and explore a novel generalization of causal abstractions

Problem

• Develops a novel semantics for counterfactual probabilities beyond Pearl's framework
• Addresses limitations in probabilistic causal models lacking realistic structural extensions
• Proposes a compromise between Pearl and Dawid on counterfactual semantics

Innovation

• Generalizes Pearlian semantics for probabilistic causal models
• Uses Markov condition with realistic variables, no response variables
• Equivalent to recent non-structural causal model proposals