For solving logical implication problem in the presence of XML strong multi-valued dependency(denoted as XSMVD) and XML weak multi-valued dependency(denoted as XWMVD) under incomplete information circumstances, the inference rules of XSMVD and XWMVD based on XML Schema were discussed. The concepts of XML Schema and incomplete XML document tree according with XML Schema were formalized. Based on the concepts of sub-tree information equivalence and sub-tree information consistent, the definitions of XSMVD and XWMVD were given and their nature was studied. When XSMVD and XWMVD exist at the same time in XML Schema, their inference rules were presented and their soundness was proved. The production in this work lays the foundation for normalization of XML Schema existing XSMVD and XWMVD at the same time under incomplete information circumstances.