Probabilistic Reasoning across the Causal Hierarchy

2020/01/09 by Duligur Ibeling, Thomas Icard, Ibeling, Duligur +1 · 5 citations
Computer Science · Mathematics · Psychology · #Artificial Intelligence (cs.AI) #Artificial intelligence #Bayesian Modeling and Causal Inference #Bayesian network #Computer science #Conditional independence #Counterfactual conditional #Counterfactual thinking #Decidability #Discrete mathematics #FOS: Computer and information sciences #Finitary #Hierarchy #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Mathematics #Probabilistic argumentation #Probabilistic logic #Psychology #Satisfiability #Semantic Web and Ontologies #Situation calculus #Theoretical computer science #cs.AI #cs.LO

paper · pdf · doi:10.48550/arxiv.2001.02889

published in arXiv (Cornell University) (Cornell University) · AAAI-20

openalex publication_date 2020/01/09 · arxiv created 2021/06/02 · arxiv updated 2021/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

Cited by

• Gateways to Tractability for Satisfiability in Pearl's Causal Hierarchy
• A Distributional Perspective on Pearl's Causal Hierarchy: From Marginal to Joint and Individualized Potential Outcomes
• Position: Causal Machine Learning Requires Rigorous Synthetic Experiments for Broader Adoption
• The Logic of Dynamical Systems Is Relevant
• Probabilistic and Causal Satisfiability: Constraining the Model

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