{"type":"ScholarlyArticle","title":"Mixed-World Reasoning with Existential Rules under Active-Domain Semantics","authors":[{"name":"Meghyn Bienvenu","slug":"meghyn-bienvenu","given":"Meghyn","family":"Bienvenu","affiliation":"CNRS , LaBRI , University of Bordeaux and Bordeaux INP , Talence , France"},{"name":"Pierre Bourhis","slug":"pierre-bourhis","given":"Pierre","family":"Bourhis","affiliation":"CNRS , CRIStAL , University of Lille , Centrale Lille and INRIA Lille , Lille , France"}],"abstract":"In this paper, we study reasoning with existential rules in a setting where some of the predicates may be closed (i.e., their content is fully specified by the data instance) and the remaining open predicates are interpreted under active-domain semantics. We show, unsurprisingly, that the main reasoning tasks (satisfiability and certainty / possibility of Boolean queries) are all intractable in data complexity in the general case. However, several positive (PTIME data) results are obtained for the linear fragment, and interestingly, these tractability results hold also for various extensions, e.g., with negated closed atoms and disjunctive rule heads. This motivates us to take a closer look at the linear fragment, exploring its expressivity and defining a fixpoint extension to approximate non-linear rules.","doi":"10.24963/ijcai.2019/216","url":"https://ijcai.org/proceedings/2019/216","pdf":"https://ijcai.org/proceedings/2019/0216.pdf","markdown":"https://ijcai.org/proceedings/2019/216.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/216","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":"Knowledge Representation and Reasoning","track":"Main track","number":216,"pages":{"first":1558,"last":1565},"keywords":["Knowledge Representation and Reasoning: Computational Complexity of Reasoning","Knowledge Representation and Reasoning: Description Logics and Ontologies","Knowledge Representation and Reasoning: Knowledge Representation Languages","Multidisciplinary Topics and Applications: Intelligent Database Systems"],"videos":[],"references":[{"position":1,"raw":"[Abiteboul and Vianu, 1991] Serge Abiteboul and Victor Vianu. 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