During the metadata creation based on Common Warehouse Metamodel(CWM), the different experiences and views of describing data of organizations involved in metadata creation bring metadata on 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 lack precise semantics. In this paper, we formalize and reason on CWM metamodel and metadata in terms of a logic belonging to Description Logics, which are subsets of First-Order Logic. We distinguish consistency into horizontal consistency and evolution consistency. Towards evolution consistency, we extend CWM metamodel with version capabilities so that reasoning about inconsistency caused by evolution can be done. Then reasoning engine LOOM is applied to check consistency for the above two situations, the results are encouraging.