Description Logics with Abstraction and Refinement

• URL: http://arxiv.org/abs/2306.03717v3
• Date: Fri, 20 Oct 2023 13:42:57 GMT
• Title: Description Logics with Abstraction and Refinement
• Authors: Carsten Lutz, Lukas Schulze
• Abstract summary: We propose an extension of description logics (DLs) in which abstraction levels are first-class citizens. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable.
• Score: 8.958066641323894
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens and which provides explicit operators for the abstraction and refinement of concepts and roles across multiple abstraction levels, based on conjunctive queries. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable. We also pinpoint the precise complexity of our logics and several relevant fragments.

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