In the process of building data warehouse based on Data Vault (DV), the creation and use of metadata involve multiple schemas and views of data from different sources, which inevitably bring inconsistency problems such as metadata missing, duplication and disconnection. However, due to the lack of precise semantics in DV metamodel, it is difficult to use automatic logical reasoning to detect these problems. This paper presents a formal logic DL _dv in the describing logic family. Formalization upon the metamodel and metadata of DV data warehouse are analyzed in detail by using the descriptive logic DL _dv . It is proved that the feasibility of applying DL _dv to DV metamodel for automatically consistency reasoning.