{"type":"ScholarlyArticle","title":"Strong Inconsistency in Nonmonotonic Reasoning","authors":[{"name":"Gerhard Brewka","slug":"gerhard-brewka","given":"Gerhard","family":"Brewka","affiliation":"Department of Computer Science , Leipzig University , Germany"},{"name":"Matthias Thimm","slug":"matthias-thimm","given":"Matthias","family":"Thimm","affiliation":"Institute for Web Science and Technologies (WeST) , University of Koblenz-Landau , Germany"},{"name":"Markus Ulbricht","slug":"markus-ulbricht","given":"Markus","family":"Ulbricht","affiliation":"Department of Computer Science , Leipzig University , Germany"}],"abstract":"Minimal inconsistent subsets of knowledge bases play an important role in classical logics, most notably for repair and inconsistency measurement. It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency. We show that—in an arbitrary logic, monotonic or not—minimal strongly inconsistent subsets play the same role as minimal inconsistent subsets in classical reasoning. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics if the strong notion of inconsistency is used. We investigate the complexity of various related reasoning problems and present a generic algorithm for computing minimal strongly inconsistent subsets of a knowledge base. We also demonstrate the potential of our new notion for applications, focusing on repair and inconsistency measurement.","doi":"10.24963/ijcai.2017/125","url":"https://ijcai.org/proceedings/2017/125","pdf":"https://ijcai.org/proceedings/2017/0125.pdf","markdown":"https://ijcai.org/proceedings/2017/125.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/125","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":125,"pages":{"first":901,"last":907},"keywords":["Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation","Knowledge Representation, Reasoning, and Logic: Non-monotonic Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Agrawal and Srikant, 1994] Rakesh Agrawal and Ramakr- ishnan Srikant. 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