Embedded Cardinality Constraints

Cardinality constraints express bounds on the number of data patterns that occur in application domains. They improve the consistency dimension of data quality by enforcing these bounds within database systems. Much research has examined the semantics of integrity constraints over incomplete relations in which null markers can occur. Unfortunately, relying on some fixed interpretation of null markers leads frequently to doubtful results. We introduce the class of embedded cardinality constraints which hold on incomplete relations independently of how null marker occurrences are interpreted. Two major technical contributions are made as well. Firstly, we establish an axiomatic and an algorithmic characterization of the implication problem associated with embedded cardinality constraints. This enables humans and computers to reason efficiently about such business rules. Secondly, we exemplify the occurrence of embedded cardinality constraints in real-world benchmark data sets both qualitatively and quantitatively. That is, we show how frequently they occur, and exemplify their semantics.