Completion Rules for Uncertainty Reasoning with the Description Logic ALC

Description Logics (DLs) are gaining more popularity as the foundation of ontology languages for the Semantic Web. On the other hand, uncertainty is a form of deficiency or imperfection commonly found in the real-world information/data. In recent years, there has been an increasing interest in extending the expressive power of DLs to support uncertainty, for which a number of frameworks have been proposed. In this paper, we introduce an extension of DL ( ) that unifies and/or generalizes a number of existing approaches for DLs with uncertainty. We first provide a classification of the components of existing frameworks for DLs with uncertainty in a generic way. Using this as a basis, we then discuss ways to extend these components with uncertainty, which includes the description language, the knowledge base, and the reasoning services. Detailed explanations and examples are included to describe the proposed completion rules.