{"type":"ScholarlyArticle","title":"A Modal Characterization Theorem for a Probabilistic Fuzzy Description Logic","authors":[{"name":"Paul Wild","slug":"paul-wild","given":"Paul","family":"Wild","affiliation":"Friedrich-Alexander-Universität Erlangen- Nürnberg"},{"name":"Lutz Schröder","slug":"lutz-schroder","given":"Lutz","family":"Schröder","affiliation":"Friedrich-Alexander-Universität Erlangen- Nürnberg"},{"name":"Dirk Pattinson","slug":"dirk-pattinson","given":"Dirk","family":"Pattinson","affiliation":"Australian National University , Canberra"},{"name":"Barbara König","slug":"barbara-konig","given":"Barbara","family":"König","affiliation":"Universität Duisburg-Essen"}],"abstract":"The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.","doi":"10.24963/ijcai.2019/263","url":"https://ijcai.org/proceedings/2019/263","pdf":"https://ijcai.org/proceedings/2019/0263.pdf","markdown":"https://ijcai.org/proceedings/2019/263.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/263","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Knowledge Representation and Reasoning","track":"Main track","number":263,"pages":{"first":1900,"last":1906},"keywords":["Knowledge Representation and Reasoning: Non-classical Logics for Knowledge Representation","Uncertainty in AI: Uncertainty in AI","Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief","Knowledge Representation and Reasoning: Description Logics and Ontologies"],"videos":[],"references":[{"position":1,"raw":"[Baldan et al., 2014] Paolo Baldan, Filippo Bonchi, Henning Kerstan, and Barbara König. 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