{"type":"ScholarlyArticle","title":"The Hardness of Reasoning about Probabilities and Causality","authors":[{"name":"Benito van der Zander","slug":"benito-van-der-zander","given":"Benito","family":"van der Zander","affiliation":"Institute of Theoretical Computer Science , University of Lübeck , Germany"},{"name":"Markus Bläser","slug":"markus-blaser","given":"Markus","family":"Bläser","affiliation":"Saarland University , Saarland Informatics Campus , Saarbrücken , Germany"},{"name":"Maciej Liśkiewicz","slug":"maciej-liskiewicz","given":"Maciej","family":"Liśkiewicz","affiliation":"Institute of Theoretical Computer Science , University of Lübeck , Germany"}],"abstract":"We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. \r\nWe focus on satisfiability problems whose instance formulas allow expressing many tasks in probabilistic and causal inference.  \r\nThe main contribution of this work is establishing the exact computational complexity of these satisfiability problems. \r\nWe introduce a new natural complexity class, named succ∃R, which can be viewed as a succinct variant of the well-studied class ∃R, and show that these problems are complete for succ∃R. \r\nOur results imply even stronger limitations on the use of algorithmic methods for reasoning about probabilities and causality than  previous state-of-the-art results that rely only on the NP- or ∃R-completeness of the satisfiability problems for some restricted languages.","doi":"10.24963/ijcai.2023/636","url":"https://ijcai.org/proceedings/2023/636","pdf":"https://ijcai.org/proceedings/2023/0636.pdf","markdown":"https://ijcai.org/proceedings/2023/636.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/636","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Uncertainty in AI","track":"Main Track","number":636,"pages":{"first":5730,"last":5738},"keywords":["Knowledge Representation and Reasoning: KRR: Causality","Uncertainty in AI: UAI: Causality, structural causal models and causal inference","Machine Learning: ML: Causality"],"videos":[],"references":[{"position":1,"raw":"[Abadi and Halpern, 1994] Martin Abadi and Joseph Y Halpern. 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