Functional, Transitive, and Multivalued Compatibilities | Teradata Vantage - Functional, Transitive, and Multivalued Compatibilities - Advanced SQL Engine - Teradata Database

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":

Inference Axioms for Functional Dependencies

The concept of functional dependencies for relations produced a complete set of inference axioms for functional and multivalued dependencies for relations. These axioms are described in the following table:

The following table lists many of the dependencies among these attributes implied by the inference axioms:

Inference Axioms for Multivalued Dependencies

The following table lists the complete set of multivalued dependencies: