{"type":"ScholarlyArticle","title":"Safe Inductions: An Algebraic Study","authors":[{"name":"Bart Bogaerts","slug":"bart-bogaerts","given":"Bart","family":"Bogaerts","affiliation":"KU Leuven , Department of Computer Science Celestijnenlaan 200A , Leuven , Belgium; tion -Flanders (FWO) ."},{"name":"Joost Vennekens","slug":"joost-vennekens","given":"Joost","family":"Vennekens","affiliation":"KU Leuven , Department of Computer Science Celestijnenlaan 200A , Leuven , Belgium"},{"name":"Marc Denecker","slug":"marc-denecker","given":"Marc","family":"Denecker","affiliation":"KU Leuven , Department of Computer Science Celestijnenlaan 200A , Leuven , Belgium"}],"abstract":"In many knowledge representation formalisms, a constructive semantics is defined based on sequential applications of rules or of a semantic operator. These constructions often share the property that rule applications must be delayed until it is safe to\r\ndo so: until it is known that the condition that triggers the rule will remain to hold. This intuition occurs for instance in the well-founded semantics of logic programs and in autoepistemic logic. \r\nIn this paper, we formally define the safety criterion  algebraically. We study properties of so-called safe inductions and apply our theory to logic programming and autoepistemic logic. For the latter, we show that safe inductions manage to capture the intended meaning of a class of theories on which all classical constructive semantics fail.","doi":"10.24963/ijcai.2017/119","url":"https://ijcai.org/proceedings/2017/119","pdf":"https://ijcai.org/proceedings/2017/0119.pdf","markdown":"https://ijcai.org/proceedings/2017/119.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/119","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":119,"pages":{"first":859,"last":865},"keywords":["Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation","Knowledge Representation, Reasoning, and Logic: Non-monotonic Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Antic et al., 2013] Christian Antic, Thomas Eiter, and Michael Fink. 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