Understanding the concept of "completeness" in frameworks for modeling cardinality constraints

Cardinality constraints have been a useful and integral part of conceptual database design since the original entity-relationship (ER) model proposed by Chen. Subsequently many papers discussing classification frameworks for cardinality constraints have been proposed. Completeness of such frameworks has always been in question since well-defined criteria do not exist to evaluate them. We propose a "reverse engineering" approach, i.e., one of defining conceptual modeling constraint completeness based on mappings from the relational model. We develop a correspondence for combinations of relational algebra operators to existing semantic constraint types. In doing so, we also come up with a new category of cardinality constraints not previously examined in literature. We feel our work has useful implications from a semantics perspective, and more importantly from a practical standpoint in developing automated mechanisms for implementing cardinality constraints.