{"type":"ScholarlyArticle","title":"Making Cross Products and Guarded Ontology Languages Compatible","authors":[{"name":"Pierre Bourhis","slug":"pierre-bourhis","given":"Pierre","family":"Bourhis","affiliation":"CRIStAL , CNRS & Université Lille 1 , France"},{"name":"Michael Morak","slug":"michael-morak","given":"Michael","family":"Morak","affiliation":"Institute of Information Systems , TU Wien , Austria"},{"name":"Andreas Pieris","slug":"andreas-pieris","given":"Andreas","family":"Pieris","affiliation":"School of Informatics , University of Edinburgh , UK"}],"abstract":"Cross products form a useful modelling tool that allows us to express natural statements such as \"elephants are bigger than mice\", or, more generally, to define relations that connect every instance in a relation with every instance in another relation. Despite their usefulness, cross products cannot be expressed using existing guarded ontology languages, such as description logics (DLs) and guarded existential rules. The question that comes up is whether cross products are compatible with guarded ontology languages, and, if not, whether there is a way of making them compatible. This has been already studied for DLs, while for guarded existential rules remains unanswered. Our goal is to give an answer to the above question. To this end, we focus on the guarded fragment of first-order logic (which serves as a unifying framework that subsumes many of the aforementioned ontology languages) extended with cross products, and we investigate the standard tasks of satisfiability and query answering. Interestingly, we isolate relevant fragments that are compatible with cross products.","doi":"10.24963/ijcai.2017/122","url":"https://ijcai.org/proceedings/2017/122","pdf":"https://ijcai.org/proceedings/2017/0122.pdf","markdown":"https://ijcai.org/proceedings/2017/122.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/122","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":122,"pages":{"first":880,"last":886},"keywords":["Knowledge Representation, Reasoning, and Logic: Description Logics and Ontologies","Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation","Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Amarilli et al., 2016] Antoine Amarilli, Michael Benedikt, Pierre Bourhis, and Michael Vanden Boom. 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