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Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.<\/jats:p><jats:p>We start by investigating a notion of<jats:italic>defeasible subsumption<\/jats:italic>in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both<jats:italic>preferential<\/jats:italic>and<jats:italic>rational<\/jats:italic>subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of<jats:italic>entailment<\/jats:italic>and present an algorithm for the computation of<jats:italic>rational closure<\/jats:italic>of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL<jats:italic>ALC<\/jats:italic>.<\/jats:p>","DOI":"10.1145\/3420258","type":"journal-article","created":{"date-parts":[[2020,11,25]],"date-time":"2020-11-25T01:20:16Z","timestamp":1606267216000},"page":"1-46","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":19,"title":["Principles of KLM-style Defeasible Description Logics"],"prefix":"10.1145","volume":"22","author":[{"given":"Katarina","family":"Britz","sequence":"first","affiliation":[{"name":"CAIR, Stellenbosch University, South Africa"}]},{"given":"Giovanni","family":"Casini","sequence":"additional","affiliation":[{"name":"ISTI-CNR, Italy and CAIR, University of Cape Town, South Africa"}]},{"given":"Thomas","family":"Meyer","sequence":"additional","affiliation":[{"name":"CAIR, University of Cape Town, South Africa"}]},{"given":"Kody","family":"Moodley","sequence":"additional","affiliation":[{"name":"Institute of Data Science, Maastricht University, Netherlands"}]},{"given":"Uli","family":"Sattler","sequence":"additional","affiliation":[{"name":"Information Management Group, University of Manchester, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0025-9632","authenticated-orcid":false,"given":"Ivan","family":"Varzinczak","sequence":"additional","affiliation":[{"name":"CRIL, Univ. Artois 8 CNRS, France and CAIR, Computer Science Division, Stellenbosch University, South Africa"}]}],"member":"320","published-online":{"date-parts":[[2020,11,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"F. Baader D. Calvanese D. McGuinness D. Nardi and P. Patel-Schneider (Eds.). 2007. The Description Logic Handbook: Theory Implementation and Applications (2nd ed.). Cambridge University Press. F. Baader D. Calvanese D. McGuinness D. Nardi and P. Patel-Schneider (Eds.). 2007. The Description Logic Handbook: Theory Implementation and Applications (2nd ed.). Cambridge University Press.","DOI":"10.1017\/CBO9780511711787"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI\u201993)","author":"Baader F.","unstructured":"F. Baader and B. Hollunder . 1993. How to prefer more specific defaults in terminological default logic . 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