{"type":"ScholarlyArticle","title":"Abducing Relations in Continuous Spaces","authors":[{"name":"Taisuke Sato","slug":"taisuke-sato","given":"Taisuke","family":"Sato","affiliation":"AI research center AIST , Japan"},{"name":"Katsumi Inoue","slug":"katsumi-inoue","given":"Katsumi","family":"Inoue","affiliation":"National Institute of Informatics , Japan"},{"name":"Chiaki Sakama","slug":"chiaki-sakama","given":"Chiaki","family":"Sakama","affiliation":"Wakayama University , Japan"}],"abstract":"We propose a new approach to abduction, i.e., non-deductive inference to find a hypothesis H for an observation O such that H,KB |- O where KB is background knowledge. We reformulate it linear algebraically in vector spaces to abduce ``relations'', not logical  formulas, to realize  approximate but  scalable  abduction that can deal with web-scale knowledge bases.  More specifically we consider the problem of abducing relations for Datalog programs with binary predicates.  We treat two cases, the non-recursive case and the recursive case. In the non-recursive case, given r1(X,Y) and r3(X,Z),  we abduce r2(Y,Z) so that r3(X,Z) <= r1(X,Y)&r2(Y,Z) approximately holds, by computing a matrix R2 that approximately satisfies a matrix equation R3  = min1(R1R2) containing a  nonlinear function min1(x).  Here R1, R2 andR3 encode as adjacency matrix r1(X,Y),  r2(Y,Z) and r3(Y,Z) respectively.  We apply this matrix-based abduction to rule discovery and relation discovery in a  knowledge graph.  The recursive  case is mathematically more  involved and computationally more difficult but solvable by deriving  a recursive matrix equation and  solving it.  We illustrate concrete recursive cases including a transitive closure relation.","doi":"10.24963/ijcai.2018/270","url":"https://ijcai.org/proceedings/2018/270","pdf":"https://ijcai.org/proceedings/2018/0270.pdf","markdown":"https://ijcai.org/proceedings/2018/270.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/270","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":"Knowledge Representation and Reasoning","track":"Main track","number":270,"pages":{"first":1956,"last":1962},"keywords":["Knowledge Representation and Reasoning: Knowledge Representation Languages","Machine Learning: Relational Learning","Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Bollacker et al., 2008] Kurt Bollacker, Colin Evans, Praveen Paritosh, Tim Sturge, and Jamie Taylor. 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