Constructive Interpolation and Concept-Based Beth Definability for Description Logics via Sequents
This work addresses foundational issues in knowledge representation and reasoning for description logics, offering incremental advances in proof theory and definability.
The paper tackles the problem of establishing the concept-based Beth definability property (CBP) for description logics by introducing a constructive method using sequent systems, with results including the first proof that RIQ enjoys the CBP and a novel approach to computing interpolants and definitions.
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 restrictions of RIQ, and are applicable to other DLs by suitable modifications.