Most current object-oriented database management systems (OODBMs) support a few types of dynamic schema change operations that include adding or dropping a class, and inserting or deleting an inheritance relationship to an existing schema. Although these operations can strengthen the update of OODB schema for various application purposes, they easily lead to redundant inheritance and cgclic inheritances. The former suffers from data redundancy and data inconsistency, and the latter suffers from self-inheritance, all of which increase the difficulties of class hierarchy query. In this paper, the authors explain how the changes of schema would lead to redundant and cyclic inheritance, and give a concrete example of the problems that arise. They propose a new concept called minimal class hierarchy to detect the two problems. Furthermore, a formal checking mechanism based on logical implication (often called inference rules) is proposed. A theoretical analysis shows that this checking mechanism is precise and easily implemented.
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