On Natural Joins in Object-Oriented Databases

In this paper, we introduce a recursively-defined natural join operation for composing complex objects. The notable features of our natural join are (1) Operand types are generalized into atomic-type, set-type, and tuple-type objects, and (2) The elements of set-type objects are allowed to be heterogenous. Then, we discuss how to realize the natural join by the message passing computing mechanism. Finally, we investigate some mathematical properties about the natural join. Especially, we provide a condition under which the sub-object relationship defined by Bancilhon and Khoshafian is preserved under our natural join and investigate the relationship between their intersection and our natural join.