Probabilistic Reasoning across the Causal Hierarchy
This work provides a foundational framework for causal reasoning, enabling formal analysis across different levels of causal inference.
The authors formalized the three-tier causal hierarchy (association, intervention, counterfactuals) as probabilistic logical languages with increasing expressivity, showing that satisfiability and validity for each language are decidable in polynomial space.
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.