{"type":"ScholarlyArticle","title":"Stratified Negation in 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":"There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing declarative languages for data analysis can be formalised as variants of logic programming equipped with arithmetic function symbols and/or aggregation, and are typically undecidable. In prior work, the language of limit programs was proposed, which is sufficiently powerful to capture many analysis tasks and has decidable entailment problem. Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure. We show that the additional expressive power makes reasoning computationally more demanding, and provide tight data complexity bounds. We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.","doi":"10.24963/ijcai.2018/259","url":"https://ijcai.org/proceedings/2018/259","pdf":"https://ijcai.org/proceedings/2018/0259.pdf","markdown":"https://ijcai.org/proceedings/2018/259.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/259","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":"Knowledge Representation and Reasoning","track":"Main track","number":259,"pages":{"first":1875,"last":1881},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Logics for Knowledge Representation","Knowledge Representation and Reasoning: Knowledge Representation Languages","Knowledge Representation and Reasoning: Non-monotonic Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Alvaro et al., 2010] Peter Alvaro, Tyson Condie, Neil Con- way, Khaled Elmeleegy, Joseph M. 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