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Description logics (short for DLs) are very important for the expression of ontologies, which allow reasoning about individuals and concepts. However, DLs can not process the indefinite knowledge existing widely in nature. Based on the cloud model, we present cloud-ALC to deal with the indefinite knowledge, which is the extension of the important description logic ALC. We define its syntax and semantic, study its properties in detail, and propose the techniques to solve the entailment problem. Case analysis proves that cloud-ALC can provide a formal underpinning for the indefiniteness extension of ontology description languages.