Object Functional Dependencies and the Semantics of Class Extensions

We introduce the concept of object functional dependency for object oriented models, and we study consistency, satisfaction and functional implication in the context of a class extension. We then use functional implication to deene the formal semantics of a class extension by a least xpoint construction. The concepts introduced here are motivated by similar and well known concepts of the relational model. However, their deenition in the context of a class extension requires a \dual" approach to the one used in object oriented models. Namely, instead of considering each object of a class extension associated to a tuple of values over the class attributes, we consider each class attribute associated to a tuple of values over the objects of the class extension. One important aspect of our work is the clear separation between the concepts of consistency and satisfaction, something that the traditional tuples-as-functions approach of the relational model has not been able to achieve. Another important aspect of our work is that, by looking at attributes as functions over the object identiiers, we can extend our results in two directions : (a) We can allow attribute values to be object identiiers, thus creating \at-tribute paths". (b) We can then consider extending the notion of attribute dependency seen here, to that of attribute-path dependency.