During the metadata creation based on common warehouse metamodel (CWM), the different experiences and views of describing data of organizations involved in metadata creation cause some problems inevitably, such as inconsistencies and redundancies. However, reasoning on CWM metadata for automatically detecting these problems is difficult because CWM metamodel and metadata are rendered to users by graphs, which lack precise semantics. In this paper, an approach is proposed to formalize and reason on CWM metamodel and metadata in terms of a logic belongingto description logics, which are subsets of first-order logic. First, accordingto the specialities of CWM metamodel and metadata, description logic DL\-id which supports identification constraints on concepts is proposed. Then consistency is distinguished into horizontal consistency and evolution consistency. Towards evolution consistency, CWM metamodel is extended with version capabilities so that reasoning about inconsistency caused by evolution can be done and then the formalization of CWM metamodel and metadata into DL\-id knowledge base for horizontal consistency checking and evolution consistency checking is studied. Finally, reasoning engine LOOM is applied to check consistency for the above two situations, and the results are encouraging. The approach can be exploited for developing intelligent system that supports automated reasoning on CWM metadata, so as to provide support for the development of the components of data warehouse systems, thus improving the reliability of metadata integration and data warehouse system.