@article{Ibeling_Icard_2020, title={Probabilistic Reasoning Across the Causal Hierarchy}, volume={34}, url={https://ojs.aaai.org/index.php/AAAI/article/view/6577}, DOI={10.1609/aaai.v34i06.6577}, abstractNote={<p>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 reasoningâ€”including conditional independence and Bayesian inferenceâ€”the second encoding <em>do</em>-calculus reasoning for causal effects, and the third capturing a fully expressive <em>do</em>-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.</p>}, number={06}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Ibeling, Duligur and Icard, Thomas}, year={2020}, month={Apr.}, pages={10170-10177} }