Inclusion Dependencies

Abstract

The next dependency we will discuss is neither uni-relational nor many-sorted. A great deal of research has gone into understanding single relations, whether they are designed properly. Much less is known about how the relations should fit together. In general, an inclusion dependency (IND) is of the form

$${\text{R < A}}_{\text{1}} {\text{,}}...{\text{,A}}_{\text{m}} {\text{ > }}\underline {\text{c}} {\text{S < B}}_{\text{1}} {\text{,}}...{\text{,B}}_{\text{m}} {\text{ > }}$$

where R and S are predicates (or relation scheme names), and the A₁’s and B₁’s are attributes of the corresponding schemes. The inclusion dependency holds for a database if each tuple that is a member of the relation corresponding to the left-hand side is also in the relation corresponding to the right-hand side. Hence, IND’s are valuable for database design, since they permit us to selectively define what data must be duplicated in what relations. IND’s, together with FD’s, are perhaps the most important integrity constraints for relational databases. Although IND’s have been extensively utilized for databases, they only recently were subject of theoretical investigations. Their expressive power is not utilized yet. They could, for instance, play a more important role in management of distributed databases (replication).