{"type":"ScholarlyArticle","title":"Classification Transfer for Qualitative Reasoning Problems","authors":[{"name":"Manuel Bodirsky","slug":"manuel-bodirsky","given":"Manuel","family":"Bodirsky","affiliation":"Institut für Algebra , TU Dresden , Germany"},{"name":"Peter Jonsson","slug":"peter-jonsson","given":"Peter","family":"Jonsson","affiliation":"Dept. of Computer and Information Science , Linköpings Universitet , Sweden"},{"name":"Barnaby Martin","slug":"barnaby-martin","given":"Barnaby","family":"Martin","affiliation":"Dept. of Computer Science , Durham University , UK"},{"name":"Antoine Mottet","slug":"antoine-mottet","given":"Antoine","family":"Mottet","affiliation":"Institut für Algebra , TU Dresden , Germany"}],"abstract":"We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use of primitive positive (pp) interpretations and pp-homotopy. We demonstrate the methodology by giving a full complexity classification of all constraint languages that are first-order definable in Allen's Interval Algebra and contain the basic relations (s) and (f). In the case of the Rectangle Algebra we answer in the affirmative the old open question as to whether ORD-Horn is a maximally tractable subset among the (disjunctive, binary) relations. We then generalise our results for the Rectangle Algebra to the r-dimensional Block Algebra.","doi":"10.24963/ijcai.2018/175","url":"https://ijcai.org/proceedings/2018/175","pdf":"https://ijcai.org/proceedings/2018/0175.pdf","markdown":"https://ijcai.org/proceedings/2018/175.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/175","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Constraints and SAT","track":"Main track","number":175,"pages":{"first":1256,"last":1262},"keywords":["Constraints and SAT: Constraint Satisfaction","Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Ahlbrandt and Ziegler, 1986] Gisela Ahlbrandt and Martin Ziegler. 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