Database Reference
In-Depth Information
Relation
R9
, though in BCNF, is not in 4NF, because it has a peculiar dependency,
called a
multi-valued dependency
(MVD). In order to state the 4NF, we must first
define MVD.
4.9.1 Multi-valued Dependency
A multi-valued dependency (MVD) is defined as follows:
Please note the following points arising from the definition of an MVD:
1.
For MVD, at least three attributes must exist.
2.
FDs are MVDs but MVDs are not necessarily FDs.
3.
A
-»
B reads “A multi-determines B” or “B is multi-dependent
on A.”
Let us get back to
R9
:
Course -» Text/Teacher
. Note that
Course
is the pivot of
the MVD.
Course -» Teacher
since
Teacher
depends on Course, independent of Text.
Course
-»
Text
since
Text
depends on
Course
, independent of
Teacher
.
4.9.2 Fagin's Theorem
Fagin's theorem (named after Ronald Fagin who proposed it) may be stated as follows:
Note that like Heath's theorem, which prescribes how to treat FDs, Fagin's theorem
states exactly how to treat MVDs. With this background, we can proceed to defining the 4NF:
