{"type":"ScholarlyArticle","title":"Cone Semantics for Logics with Negation","authors":[{"name":"Özgür Lütfü Özçep","slug":"ozgur-lutfu-ozcep","given":"Özgür","family":"Lütfü Özçep","affiliation":"University of Lübeck , Germany"},{"name":"Mena Leemhuis","slug":"mena-leemhuis","given":"Mena","family":"Leemhuis","affiliation":"University of Lübeck , Germany"},{"name":"Diedrich Wolter","slug":"diedrich-wolter","given":"Diedrich","family":"Wolter","affiliation":"University of Bamberg , Germany"}],"abstract":"This paper presents an embedding of ontologies expressed in the ALC description logic into a real-valued vector space, comprising restricted existential and universal quantifiers, as well as concept negation and concept disjunction. Our main result states that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a partial faithful geometric model based on cones. The line of work to which we contribute aims to integrate knowledge representation techniques and machine learning. The new cone-model of ALC proposed in this work gives rise to conic optimization techniques for machine learning, extending previous approaches by its ability to model full ALC.","doi":"10.24963/ijcai.2020/252","url":"https://ijcai.org/proceedings/2020/252","pdf":"https://ijcai.org/proceedings/2020/0252.pdf","markdown":"https://ijcai.org/proceedings/2020/252.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/252","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":252,"pages":{"first":1820,"last":1826},"keywords":["Knowledge Representation and Reasoning: Description Logics and Ontologies","Machine Learning: Knowledge-based Learning","Knowledge Representation and Reasoning: Qualitative, Geometric, Spatial, Temporal Reasoning","Knowledge Representation and Reasoning: Other"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25030/file_25030.m3u8","length_sec":276,"provider":"hls"}],"references":[{"position":1,"raw":"[Baader and Küsters, 2006] Franz Baader and Ralf Küsters. 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