Correctness of ISA hierarchies in object-oriented database schemas

Abstract

In Object-Oriented databases, ISA hierarchy provides a powerful modeling tool that, through the inheritance mechanism, yields a coincise description of the world. In this paper, we tackle the problem of the correctness of ISA hierarchies in Object-Oriented database schemas. In general, the inheritance mechanisms proposed in literature do not preserve subtyping, i. e. they are not sound. Strict inheritance has been proposed in order to guarantee subtyping after inheritance. However, strict inheritance is sound but fails to cope with a significant class of schemas. The problem relies on refinement rules. In the paper, we characterize the schemas for which strict inheritance is sound and complete and we present a methodology aimed at identifying such schemas. The problem is addressed using the Object-Oriented data definition language TQL.