Page 122 - DCAP402_DCAO204_DATABASE MANAGEMENT SYSTEM_MANAGING DATABASE

Unit 7: Relational Database Design

1. *(R , R , . . .,R ) is a trivial join dependency. Notes
1 2 n
2. Every R is a superkey for R.
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PJNF is also referred to as the Fifth Normal Form (5NF).
Let us first define the concept of PJNF from the viewpoint of the decomposition and then refine
it later to a standard form.
Definition 1: A JD *[R , R , . . . , R ] over a relation R is trivial if it is satisfied by every
1 2 n
relation r(R).
The trivial JDs over R are JDs of the form *[R , R , . . . , R ] where for some i the R = R.
1 2 n i
Definition 2: A JD *[R , R , . . ., R ] applies to a relation scheme R if R = R R …R .
1 2 n 1 2 n
Definition 3: Let R be a relation scheme having F as the set of FDs and JDs over R. R will be in
project-join normal form (PJNF) if for every JD *[R , R , . . ., R ] which can be derived by F that
1 2 n
applies to R, the following holds:
1. The JD is trivial
2. Every R is a super key for R.
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For a database scheme to be in project-join normal form, every relation R in this database
scheme should be in project-join normal form with respect to F.
Let us explain the above with the help of an example.

Example: Consider a relational scheme R = A B C D E G having the set of dependencies
F = {*[A B C D, C D E, B D G], *[A B, B C D, A D], A B C D E, B C A G }. The R as given above
is not in PJNF. Why? The two alternate keys to R are A and BC, so please note that the JD *[A B
C D, C D E, B D G], does not satisfy the condition “Every R is a super key for R” as the two
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components of this JD viz., C D E and B D G, does not satisfy the condition.
However, if we decompose the R as {R , R , R }, where R = A B C D, R = C D E, and R = B D G,
1 2 3 1 2 3
then it is in PJNF with respect to F. Please note that in the example, the JD *[A B, B C D, A D] is
implied by F and applies to R . Whereas, the FDs are trivial or have keys as the left side.
1
The definition of PJNF as given above is a weaker than the original definition of PJNF given by
Fagin. The original definition ensures enforceability of dependencies by satisfying keys, in
addition to elimination of redundancy. The final definition is:
Definition 4: Let R be a relation scheme having F as the set of FDs and JDs over R. R will be in
project-join normal form (PJNF) if for every JD *[R , R , . . ., R ] which can be derived by F that
1 2 n
applies to R, is implied by the key FDs of R.
The following example demonstrates this definition.

Example: Consider a relation scheme R = A B C having the set of dependencies as
F = {A B C, C A B, *[A B, B C] }. Please note that the R is not in PJNF, although since A B and
B C are the super keys of R, R satisfies the earlier definition of PJNF. But R does not satisfy the
revised definition as given above.

Notes Since every multivalued dependency is also a join dependency, every PJNF schema
is also in 4NF. Decomposing a relation scheme using the JDs that cause PJNF violations
creates the PJNF scheme. PJNF may also be not dependency preserving.

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