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Context

One of the issues encountered during the design of a relational database, is the representation of the relationships between the data under consideration. This representation might allow to correctly describe the reality of the application that is being studied. These relationships require that certain data verify a set of constraints, also called dependencies. ( Dependency theory )

Definition : For any given application, only a subset of all possible relations is of interest. This subset is defined by constraints that are to be satisfied by the relations of interest. A class of constraints that has been extensively studied is the class of dependencies.

Dependency classes

There are different classes of dependencies, among which there are:

FD	functional dependencies
JD	join dependencies
MVD	multivalued dependencies
TGD	tuple-generating dependencies
EGD	equality-generating dependencies
TTGD	total tuple-generating dependencies
EMVD	embedded multivalues dependencies
EID	embededd implicational dependencies
AD	algebraic dependencies

The MVDs were introduced before the appearance of several other classes such as JD :

In general, a jd may involve more than two attribute sets. Multivalued dependency (mvd) is the special case of jd’s that have at most two attribute sets. Due to their naturalness, mvd’s were intro-duced before jd’s and have several interesting properties, which makes them worth studying on their own.

Classification

The classification of these different classes can be illustrated by this diagram, which provides a summarization of the following elements provided by Catriel BEERI et Moshe Y. Vardi  :

Classification of dependencies

• EGD (Equality-generating dependencies) generalize FDs (functional dependencies).

• TTGD (Total tuple-generating dependencies) generalize MVDs.

• The class of TTGDs and EGDs contains as special cases almost all classes of dependencies that were investigated in the literature, for example, functional (FD), multivalued (MVD), join (JD), and transitive dependencies. It is equivalent to the class of generalized dependencies of Grant and Jacobs. (...) It does not include, however, the classes of embedded multivalued dependencies (EMVD) and embedded join dependencies.

• Tuple-generating dependencies (TGD) generalize TTGDs and EMVDs.

• The class of TGDs and EGDs is equivalent to Fagin's class of embedded implicational dependencies (EID) , and is also shown in to be equivalent to the class of algebraic dependencies (AD).

Limitations of the study

This study does not include an exhaustive list of dependencies, in particular it does not involve the classes of embedded join dependencies and inclusion dependencies.