An Epistemic Operator for Description Logics
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SubjectKnowledge representation; Description logics; Epistemic operators; Nonmonotonic reasoning; Closed-world reasoning; Query languages
Description logics (also called terminological logics, or concept languages) are fragments of first-order logic that provide a formal account of the basic features of frame-based systems. However, there are aspects of frame-based systems - such as nonmonotonic reasoning and procedural rules - that cannot be characterized in a standard first-order framework. Such features are needed for real applications, and a clear understanding of the logic underlying them is necessary for principled implementations. We show how description logics enriched with an epistemic operator can formalize such aspects. The logic obtained is a fragment of a first-order nonmonotonic modal logic. We show that the epistemic operator formalizes procedural rules, as provided in many knowledge representation systems, and enables sophisticated query formulation, including various forms of closed-world reasoning. We provide an effective procedure for answering epistemic queries posed to a knowledge base expressed in a description logic and extend this procedure in order to deal with rules. We also address the computational complexity of reasoning with the epistemic operator, identifying cases in which an appropriate use of the epistemic operator can help in decreasing the complexity of reasoning
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