Abstract: For solving data redundancies and abnormal manipulation for XML documents in schema design under incomplete information circumstances, the normalization theory of XML Schema under incomplete information circumstances was discussed. The concepts of XML Schema and incomplete XML document tree according with XML Schema were formalized. Based on the equivalence of the nodes, the consistency of the nodes, the equivalence of the nodes' informalion and the consistency of the nodes' information,XML strong functional dependency's definition was given,inference rules for XMLstrong functional dependency were presented. The arithmetic of path set strong closure and membership problem was proposed, its correctness was proved and its time complication was analyzed. The definition of XML normal form under incomplete information circumstances and the corresponding arithmetic of the normalization were formalized. The production in this work removes the redundancies of datum, eliminates update anomalies and achieves better design of XML Schema.

Key words: Incomplete information, XML strong functional dependency, Path set strong closure, XML normal form under incomplete information circumstances