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### 10.5. Multi-valued Dependencies (MVD) and Fourth Normal Form (4NF)

To deal with the problem of BCNF, R. Fagin introduced the idea of multi-valued dependency (MVD) and the fourth normal form (4NF). A multi-valued dependency (MVD) is a functional dependency where the dependency may be to a set and not just a single value. It is defined as X →→ Y in relation R (X, Y, Z), if each X value is associated with a set of Y values in a way that does not depend on the Z values. Here X and Y are both subsets of R. The notation X →→ Y is used to indicate that a set of attributes of Y shows a multi-valued dependency (MVD) on a set of attributes of X.

Thus, informally, MVDs occur when two or more independent multi-valued facts about the same attribute occur ...

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