{"type":"ScholarlyArticle","title":"Classical Generalized Probabilistic Satisfiability","authors":[{"name":"Carlos Caleiro","slug":"carlos-caleiro","given":"Carlos","family":"Caleiro","affiliation":"SQIG -Instituto de Telecomunicac ¸ões DMath , Instituto Superior Técnico Universidade de Lisboa , Portugal"},{"name":"Filipe Casal","slug":"filipe-casal","given":"Filipe","family":"Casal","affiliation":"CMAF-CIO , Portugal DMath ,; Instituto Superior Técnico Universidade de Lisboa , Portugal"},{"name":"Andreia Mordido","slug":"andreia-mordido","given":"Andreia","family":"Mordido","affiliation":"INOV INESC Inovac ¸ão , Portugal"}],"abstract":"We analyze a classical generalized probabilistic satisfiability problem (GGenPSAT) which consists in deciding the satisfiability of Boolean combinations of linear inequalities involving probabilities of classical propositional formulas. GGenPSAT coincides precisely with the satisfiability problem of the probabilistic logic of Fagin et al. and was proved to be NP-complete. Here, we present a polynomial reduction of GGenPSAT to SMT over the quantifier-free theory of linear integer and real arithmetic. Capitalizing on this translation, we implement and test a solver for the GGenPSAT problem. As previously observed for many other NP-complete problems, we are able to detect a phase transition behavior for GGenPSAT.","doi":"10.24963/ijcai.2017/126","url":"https://ijcai.org/proceedings/2017/126","pdf":"https://ijcai.org/proceedings/2017/0126.pdf","markdown":"https://ijcai.org/proceedings/2017/126.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/126","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":126,"pages":{"first":908,"last":914},"keywords":["Constraints and Satisfiability: Satisfiability","Constraints and Satisfiability: Solvers and Tools","Uncertainty in AI: Exact Probabilistic Inference","Knowledge Representation, Reasoning, and Logic: Automated Reasoning and Theorem Proving"],"videos":[],"references":[{"position":1,"raw":"[Barrett et al., 2016] C. 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