{"type":"ScholarlyArticle","title":"Synthesizing Datalog Programs using Numerical Relaxation","authors":[{"name":"Xujie Si","slug":"xujie-si","given":"Xujie","family":"Si","affiliation":"University of Pennsylvania"},{"name":"Mukund Raghothaman","slug":"mukund-raghothaman","given":"Mukund","family":"Raghothaman","affiliation":"University of Pennsylvania"},{"name":"Kihong Heo","slug":"kihong-heo","given":"Kihong","family":"Heo","affiliation":"University of Pennsylvania"},{"name":"Mayur Naik","slug":"mayur-naik","given":"Mayur","family":"Naik","affiliation":"University of Pennsylvania"}],"abstract":"The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems, or performing parameter estimation in complex statistical models.\r\n\r\nIn this paper, we present Difflog, a technique to extend the logic programming language Datalog to the continuous setting. By attaching real-valued weights to individual rules of a Datalog program, we naturally associate numerical values with individual conclusions of the program. Analogous to the strategy of numerical relaxation in optimization problems, we can now first determine the rule weights which cause the best agreement between the training labels and the induced values of output tuples, and subsequently recover the classical discrete-valued target program from the continuous optimum.\r\n\r\nWe evaluate Difflog on a suite of 34~benchmark problems from recent literature in knowledge discovery, formal verification, and database query-by-example, and demonstrate significant improvements in learning complex programs with recursive rules, invented predicates, and relations of arbitrary arity.","doi":"10.24963/ijcai.2019/847","url":"https://ijcai.org/proceedings/2019/847","pdf":"https://ijcai.org/proceedings/2019/0847.pdf","markdown":"https://ijcai.org/proceedings/2019/847.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/847","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Understanding Intelligence and Human-level AI in the New Machine Learning era","track":"Understanding Intelligence and Human-level AI in the New Machine Learning era","number":847,"pages":{"first":6117,"last":6124},"keywords":["Special Track on Understanding Intelligence and Human-level AI in the New Machine Learning era: Neuro Statistical Relational Learning (Special Track on Human AI and Machine Learning)","Special Track on Understanding Intelligence and Human-level AI in the New Machine Learning era: Neural Methods in Inductive Logic Programming (Special Track on Human AI and Machine Learning)","Special Track on Understanding Intelligence and Human-level AI in the New Machine Learning era: Neuro-Symbolic methods (Special Track on Human AI and Machine Learning)"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul et al., 1995] Serge Abiteboul, Richard Hull, and Victor Vianu. 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