{"type":"ScholarlyArticle","title":"Foundations of Declarative Data Analysis Using Limit Datalog Programs","authors":[{"name":"Mark Kaminski","slug":"mark-kaminski","given":"Mark","family":"Kaminski","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Bernardo Cuenca Grau","slug":"bernardo-cuenca-grau","given":"Bernardo Cuenca","family":"Grau","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Egor V. Kostylev","slug":"egor-v-kostylev","given":"Egor V.","family":"Kostylev","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Boris Motik","slug":"boris-motik","given":"Boris","family":"Motik","affiliation":"Department of Computer Science , University of Oxford , UK"},{"name":"Ian Horrocks","slug":"ian-horrocks","given":"Ian","family":"Horrocks","affiliation":"Department of Computer Science , University of Oxford , UK"}],"abstract":"Motivated by applications in declarative data analysis, we study DatalogZ---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two fragments. In limit DatalogZ predicates are axiomatised to keep minimal/maximal numeric values, allowing us to show that fact entailment is coNExpTime-complete in combined, and coNP-complete in data complexity. Moreover, an additional stability requirement causes the complexity to drop to ExpTime and PTime, respectively. Finally, we show that stable DatalogZ can express many useful data analysis tasks, and so our results provide a sound foundation for the development of advanced information systems.","doi":"10.24963/ijcai.2017/156","url":"https://ijcai.org/proceedings/2017/156","pdf":"https://ijcai.org/proceedings/2017/0156.pdf","markdown":"https://ijcai.org/proceedings/2017/156.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/156","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":156,"pages":{"first":1123,"last":1130},"keywords":["Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation","Knowledge Representation, Reasoning, and Logic: Tractable languages and knowledge compilation","Knowledge Representation, Reasoning, and Logic: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Alvaro et al., 2010] Peter Alvaro, Tyson Condie, Neil Con- way, Khaled Elmeleegy, Joseph M. 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