Description Logics with Abstraction and Refinement
This addresses a limitation in ontology engineering for knowledge representation systems, though it appears to be an incremental extension of existing description logic frameworks.
The authors tackled the problem that description logics lack support for representing knowledge at multiple abstraction levels by extending them with first-class abstraction levels and explicit operators for abstraction/refinement based on conjunctive queries. They proved reasoning in these extended logics is decidable with precise complexity bounds, while showing some variations are undecidable.
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.