Inclusion dependencies are a generalization of referential constraints. As such, they provide the foundation upon which referential integrity is based. In common with functional dependencies (see Functional, Transitive, and Multivalued Dependencies), inclusion dependencies represent one-to-many relationships (see One-to-Many Relationships); however, inclusion dependencies typically represent relationships between relations (see Database-Level Constraints), while functional dependencies always represent relationships between the primary key of a relation variable and its attributes.
Suppose you have the following table definitions:
Using the notation R.A, where R is the name of a relation variable and A is the name of one of its attributes, you can write the following inclusion dependency:
supplier_parts.part_num → parts.part_num
This inclusion dependency states that the set of values appearing in the attribute part_num of relation variable supplier_parts must be a subset of the values appearing in the attribute part_num of relation variable parts. Notice that this defines a simple foreign key-primary key relationship, though it is only necessary, in order to write a proper referential integrity relationship, that the right hand side (RHS) indicates any candidate key of the specified relation variable, not necessarily its primary key (see Foreign Key Constraints for more information about this).
The left hand side (LHS) and RHS of a dependency relationship are not required to be a foreign key and a candidate key, respectively. This is merely required to write a correct inclusion dependency expression of a referential integrity relationship.
Inference Axioms for Inclusion Dependencies
Interference axioms for inclusion dependencies are described in the following table:
|Reflexive rule||A → A|
|Projection and Permutation rule||IF||AB → CD||THEN||A → C||AND||B → D|
|Transitivity rule||IF||A → B||AND||B → C||THEN||A → C|