{"type":"ScholarlyArticle","title":"The Finite Model Theory of Bayesian Networks: Descriptive Complexity","authors":[{"name":"Fabio Gagliardi Cozman","slug":"fabio-gagliardi-cozman","given":"Fabio Gagliardi","family":"Cozman","affiliation":"Escola Politécnica , Universidade de São Paulo"},{"name":"Denis Deratani Mauá","slug":"denis-deratani-maua","given":"Denis Deratani","family":"Mauá","affiliation":"Instituto de Matemática e Estatística , Universidade de São Paulo"}],"abstract":"We adapt the theory of descriptive complexity to Bayesian networks, to quantify the expressivity of specifications based on predicates and quantifiers. We show that Bayesian network specifications that employ  first-order quantification capture the complexity class PP; by allowing  quantification over predicates, the resulting Bayesian network specifications capture each class in the hierarchy PP^(NP^...^NP), a result that does not seem to have equivalent in the literature.","doi":"10.24963/ijcai.2018/727","url":"https://ijcai.org/proceedings/2018/727","pdf":"https://ijcai.org/proceedings/2018/0727.pdf","markdown":"https://ijcai.org/proceedings/2018/727.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/727","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":727,"pages":{"first":5229,"last":5233},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Uncertainty in AI: Relational Inference","Uncertainty in AI: Bayesian Networks"],"videos":[],"references":[{"position":1,"raw":"[Abadi and Halpern, 1994] Martín Abadi and Joseph Y. 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