Querying Circumscribed Description Logic Knowledge Bases
This work addresses a foundational gap in non-monotonic reasoning for description logics, which is incremental as it extends existing decidability results to query evaluation.
The paper tackled the problem of evaluating conjunctive queries (CQs) and unions thereof (UCQs) on circumscribed description logic knowledge bases, where decidability had not been established, and proved decidability while providing a comprehensive analysis of combined and data complexity across various description logics.
Circumscription is one of the main approaches for defining non-monotonic description logics (DLs). While the decidability and complexity of traditional reasoning tasks such as satisfiability of circumscribed DL knowledge bases (KBs) is well understood, for evaluating conjunctive queries (CQs) and unions thereof (UCQs), not even decidability had been established. In this paper, we prove decidability of (U)CQ evaluation on circumscribed DL KBs and obtain a rather complete picture of both the combined complexity and the data complexity, for DLs ranging from ALCHIO via EL to various versions of DL-Lite. We also study the much simpler atomic queries (AQs).