On the correctness of representing extended entity-relationship structures in the relational model

Abstract

Although the relational representation of Entity-Relationship (ER) structures gained extensive coverage, scarce attention has been paid to the issue of correctness for such representations. Several mappings have been proposed for the representation of both ER and extended ER (EER) structures by relational schemas. The informal nature of most of these proposals, however, does not allow a precise evaluation of their correctness, nor a comparison of the various mappings. We propose a canonical relational representation for EER structures and prove its correctness. We claim that a relational schema represents correctly an EER structure if it has equivalent information-capacity with the corresponding canonical representation. The second problem addressed by this paper is the normalization of relational schemas that represent EER structures. We examine the conditions required by this process and show that ignoring these conditions leads to erroneous analyses and inappropriate design decisions. We show that, under these conditions, the canonical relational representation of any (unrestricted) EER structure has an (information-capacity) equivalent Boyce-Codd Normal Form schema.