{"type":"ScholarlyArticle","title":"Revisiting the Notion of Extension over Incomplete Abstract Argumentation Frameworks","authors":[{"name":"Bettina Fazzinga","slug":"bettina-fazzinga","given":"Bettina","family":"Fazzinga","affiliation":"ICAR-CNR , Rende (CS) , Italy"},{"name":"Sergio Flesca","slug":"sergio-flesca","given":"Sergio","family":"Flesca","affiliation":"DIMES , University of Calabria , Rende(CS) , Italy"},{"name":"Filippo Furfaro","slug":"filippo-furfaro","given":"Filippo","family":"Furfaro","affiliation":"DIMES , University of Calabria , Rende(CS) , Italy"}],"abstract":"We revisit the notion of i-extension, i.e., the adaption of the fundamental \r\nnotion of extension to the case of incomplete Abstract \r\nArgumentation Frameworks.\r\nWe show that the definition of i-extension raises some concerns  in the \r\n\"possible\" variant, e.g., it allows even conflicting arguments \r\nto be collectively considered as members of an (i-)extension.\r\nThus, we introduce the alternative notion of i*-extension overcoming the \r\nhighlighted problems, and provide a thorough complexity characterization of the \r\ncorresponding verification problem.\r\nInterestingly, we show that the revisitation not only has beneficial effects for \r\nthe semantics, but also for the complexity: under various semantics,\r\nthe verification problem under the possible perspective moves from NP-complete \r\nto P.","doi":"10.24963/ijcai.2020/237","url":"https://ijcai.org/proceedings/2020/237","pdf":"https://ijcai.org/proceedings/2020/0237.pdf","markdown":"https://ijcai.org/proceedings/2020/237.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/237","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":237,"pages":{"first":1712,"last":1718},"keywords":["Knowledge Representation and Reasoning: Computational Models of Argument","Knowledge Representation and Reasoning: Computational Complexity of Reasoning"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24983/file_24983.m3u8","length_sec":303,"provider":"hls"}],"references":[{"position":1,"raw":"[Amgoud and Vesic, 2011] Leila Amgoud and Srdjan Vesic. 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