{"type":"ScholarlyArticle","title":"Constructive Interpolation and Concept-Based Beth Definability for Description Logics via Sequents","authors":[{"name":"Timothy S. Lyon","slug":"timothy-s-lyon","given":"Timothy S.","family":"Lyon","affiliation":"Institute of Artificial Intelligence , Technische Universität Dresden {timothy"},{"name":"Jonas Karge","slug":"jonas-karge","given":"Jonas","family":"Karge","affiliation":"Institute of Artificial Intelligence , Technische Universität Dresden {timothy"}],"abstract":"We introduce a constructive method applicable to a large number of description logics (DLs) for establishing the concept-based Beth definability property (CBP) based on sequent systems. Using the highly expressive DL RIQ as a case study, we introduce novel sequent calculi for RIQ-ontologies and show how certain interpolants can be computed from sequent calculus proofs, which permit the extraction of explicit definitions of implicitly definable concepts. To the best of our knowledge, this is the first sequent-based approach to computing interpolants and definitions within the context of DLs, as well as the first proof that RIQ enjoys the CBP. Moreover, due to the modularity of our sequent systems, our results hold for any restriction of RIQ, and are applicable to other DLs by suitable modifications.","doi":"10.24963/ijcai.2024/386","url":"https://ijcai.org/proceedings/2024/386","pdf":"https://ijcai.org/proceedings/2024/0386.pdf","markdown":"https://ijcai.org/proceedings/2024/386.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/386","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Knowledge Representation and Reasoning","track":"Main Track","number":386,"pages":{"first":3484,"last":3492},"keywords":["Knowledge Representation and Reasoning: KRR: Automated reasoning and theorem proving","Knowledge Representation and Reasoning: KRR: Description logics and ontologies"],"videos":[],"references":[{"position":1,"raw":"[Areces et al., 2008] Carlos Areces, Alexander Koller, and Kristina Striegnitz. 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