{"type":"ScholarlyArticle","title":"All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs","authors":[{"name":"Bartosz Bednarczyk","slug":"bartosz-bednarczyk","given":"Bartosz","family":"Bednarczyk","affiliation":"Computational Logic Group , TU Dresden; Institute of Computer Science , University of Wrocław"},{"name":"Robert Ferens","slug":"robert-ferens","given":"Robert","family":"Ferens","affiliation":"Institute of Computer Science , University of Wrocław"},{"name":"Piotr Ostropolski-Nalewaja","slug":"piotr-ostropolski-nalewaja","given":"Piotr","family":"Ostropolski-Nalewaja","affiliation":"Institute of Computer Science , University of Wrocław"}],"abstract":"The chase is a famous algorithmic procedure in database\r\ntheory with numerous applications in ontology-mediated query answering. \r\nWe consider static analysis of the chase termination \r\nproblem, which asks, given set of TGDs, whether the chase \r\nterminates on all input databases. The problem was recently \r\nshown to be undecidable by Gogacz et al. for \r\nsets of rules containing only ternary predicates.\r\n\r\nIn this work, we show that undecidability occurs already\r\nfor sets of single-head TGD over binary vocabularies. \r\nThis question is relevant since many real-world ontologies, e.g., \r\nthose from the Horn fragment of the popular OWL, are of this shape.","doi":"10.24963/ijcai.2020/238","url":"https://ijcai.org/proceedings/2020/238","pdf":"https://ijcai.org/proceedings/2020/0238.pdf","markdown":"https://ijcai.org/proceedings/2020/238.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/238","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":238,"pages":{"first":1719,"last":1725},"keywords":["Knowledge Representation and Reasoning: Logics for Knowledge Representation","Multidisciplinary Topics and Applications: Databases"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25131/file_25131.m3u8","length_sec":206,"provider":"hls"}],"references":[{"position":1,"raw":"[Baget et al., 2011] Jean-Franc ¸ois Baget, Michel Leclère, Marie-Laure Mugnier, and Eric Salvat. 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