A Formal Approach to the Definition and the Design of Conceptual Schemata for Databased Systems

Abstract

A formal approach is proposed to the definition and the design of conceptual database diagrams to be used as conceptual schemata in a system featuring a multilevel schema architecture, and as an aid for the design of other forms of schemata. We consider E-R (entity-relationship) diagrams, and we introduce a new representation called CAZ-graphs. A rigorous connection is established between these diagrams and some formal constraints used to describe relationships in the framework of the relational data model. These include functional and multivalued dependencies of database relations. The basis for our schemata is a combined representation for two fundamental structures underlying every relation: the first defined by its minimal atomic decompositions, the second by its elementary functional dependencies.The interaction between these two structures is explored, and we show that, jointly, they can represent a wide spectrum of database relationships, of which the well-known one-to-one, one-to-many, and many-to-many associations constitute only a small subset. It is suggested that a main objective in conceptual schema design is to ensure a complete representation of these two structures. A procedure is presented to design schemata which obtain this objective while eliminating redundancy. A simple correspondence between the topological properties of these schemata and the structure of multivalued dependencies of the original relation is established. Various applications are discussed and a number of illustrative examples are given. © 1982, ACM. All rights reserved.