{"type":"ScholarlyArticle","title":"Temporal Datalog with Existential Quantification","authors":[{"name":"Matthias Lanzinger","slug":"matthias-lanzinger","given":"Matthias","family":"Lanzinger","affiliation":"Department of Computer Science , University of Oxford"},{"name":"Markus Nissl","slug":"markus-nissl","given":"Markus","family":"Nissl","affiliation":"TU Wien"},{"name":"Emanuel Sallinger","slug":"emanuel-sallinger","given":"Emanuel","family":"Sallinger","affiliation":"Department of Computer Science , University of Oxford; TU Wien"},{"name":"Przemysław A. Wałęga","slug":"przemys-aw-a-wa-ega","given":"Przemysław A.","family":"Wałęga","affiliation":"Department of Computer Science , University of Oxford"}],"abstract":"Existential rules, also known as tuple-generating dependencies (TGDs) or Datalog+/- rules, are heavily studied in the communities of  Knowledge Representation and Reasoning, Semantic Web, and Databases, due to their rich modelling capabilities. In this paper we consider TGDs in the temporal setting, by introducing and studying DatalogMTLE---an extension of metric temporal Datalog (DatalogMTL) obtained by allowing for existential rules in  programs.  We show that DatalogMTLE is undecidable even in the restricted cases of guarded and weakly-acyclic programs. To address this issue we introduce uniform semantics which, on the one hand, is well-suited for modelling temporal knowledge as it prevents from unintended value invention and, on the other hand, provides decidability of reasoning; in particular, it becomes 2-EXPSPACE-complete for weakly-acyclic programs but remains undecidable for guarded programs. We provide an implementation for the decidable case  and demonstrate its practical feasibility.\r\nThus we obtain an expressive, yet decidable,  rule-language and a system which is suitable for complex temporal reasoning with existential rules.","doi":"10.24963/ijcai.2023/365","url":"https://ijcai.org/proceedings/2023/365","pdf":"https://ijcai.org/proceedings/2023/0365.pdf","markdown":"https://ijcai.org/proceedings/2023/365.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/365","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":365,"pages":{"first":3277,"last":3285},"keywords":["Knowledge Representation and Reasoning: KRR: Knowledge representation languages","Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning","Knowledge Representation and Reasoning: KRR: Qualitative, geometric, spatial, and temporal reasoning"],"videos":[],"references":[{"position":1,"raw":"[Amarilli et al., 2018] Antoine Amarilli, Michael Benedikt, Pierre Bourhis, and Michael Vanden Boom. 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