Functional, Transitive, and Multivalued Dependencies
Definitions
|
Term |
Definition |
|
Determinant |
For any relation R, the set of attributes X in the functional dependency X → Y is the determinant group for the dependency. |
|
Full functional dependence |
An attribute set X is fully functionally dependent on another attribute set Y if X is functionally dependent on the whole set of Y, but not on any subset of Y. |
|
Functional dependence |
For any relation R, attribute X is functionally dependent on attribute Y if for every valid instance, the value of Y determines the value of X. The symbolic notation for this is Y → X. |
|
Multivalued dependence |
For any relation R with attribute set (X,Y,Z), the set X multivalue determines the set Y if, for every pair of tuples containing duplicates in X, the instance also contains the pair of tuples obtained by interchanging the Y tuples in the original pair. The symbolic notation for this is X ⇒ Y. |
|
Transitive dependence |
Transitive dependencies are dependencies that exist among three or more attributes in a relation in such a way that one attribute determines a third by way of an intermediate attribute. For example, consider the relation R(X,Y,Z), where X is the primary key. Attribute Z is transitively dependent on attribute X if attribute Y satisfies the following dependencies, where the symbol → indicates does not determine: |