Probabilistic Reasoning across the Causal Hierarchy

2020/01/09 by Ibeling, Duligur, Icard, Thomas · 3 citations
#Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2001.02889

Abstract

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.

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