On the realizability of cardinality constraints in conceptual data models
A new property of conceptual data models is introduced. Realizability extends strong satisfiability as defined by Lenzerini and Nobili, which is held by a data model when it must be possible to create at least one non-empty database in which no cardinality constraints are violated. A constraint is realizable when at least one database can be created in which the number of associations involving a specific entity instance is equal to the limit imposed by the constraint. When all constraints in a data model are realizable, then the entire model is said to be realizable. It is possible for a data model to be strongly satisfiable but not realizable, which means the latter is a more stringent test for model correctness. We define bounds imposed by cardinality constraints on the relative sizes of entity sets. A data model is shown to be realizable if and only if the bounds for any cycle of relationships are either both equal to one, or the lower bound is strictly less than one while the upper bound is strictly greater than one.