{"type":"ScholarlyArticle","title":"Consistency and Set Intersection","authors":[{"name":"Yuanlin Zhang","slug":"yuanlin-zhang","given":"Yuanlin","family":"Zhang","affiliation":""},{"name":"Roland H. C. Yap","slug":"roland-h-c-yap","given":"Roland H.C.","family":"Yap","affiliation":""}],"abstract":"We propose a new framework to study properties of consistency in a Constraint Network from the perspective of properties of set intersection. Our framework comes with a proof schema which gives a generic way of lifting a set intersection property to one on consistency. Various well known results can be derived with this framework. More importantly, we use the framework to obtain a number of new results. We identify a new class of tree convex constraints where local consistency ensures global consistency. Another result is that in a network of arbitrary constraints, local consistency implies global consistency whenever there are certain m-tight constraints. The most interesting result is that when the constraint on every pair of variables is properly m-tight in an arbitrary network, global consistency can be achieved by enforcing relational m+ !-consistency. These results significantly improve our understanding of convex and tight constraints. This demonstrates that our framework is a promising and powerful tool for studying consistency.","doi":null,"url":"https://ijcai.org/proceedings/2003/39","pdf":"https://ijcai.org/proceedings/2003/0039.pdf","markdown":"https://ijcai.org/proceedings/2003/39.md","bibtex":"https://ijcai.org/proceedings/2003/bibtex/39","volume":{"slug":"2003","title":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2003","url":"https://ijcai.org/proceedings/2003/","year":2003,"location":"Acapulco, Mexico","dates":"","editors":"Georg Gottlob","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":39,"pages":{"first":263,"last":269},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}