Sixth normal form

Sixth normal form (6NF) is a term in relational database theory, used in two different ways.

6NF (C. Date's definition)

Christopher J. Date and others have defined sixth normal form as a normal form, based on an extension of the relational algebra.[1][2][3]

Relational operators, such as join, are generalized to support a natural treatment of interval data, such as sequences of dates or moments in time, for instance in temporal databases.[4][2][3] Sixth normal form is then based on this generalized join, as follows:

A relvar R [table] is in sixth normal form (abbreviated 6NF) if and only if it satisfies no nontrivial join dependencies at all — where, as before, a join dependency is trivial if and only if at least one of the projections (possibly U_projections) involved is taken over the set of all attributes of the relvar [table] concerned.[5]

Date et al. have also given the following definition:

Relvar R is in sixth normal form (6NF) if and only if every JD [Join Dependency] of R is trivial — where a JD is trivial if and only if one of its components is equal to the pertinent heading in its entirety.[6]

Any relation in 6NF is also in 5NF.

Sixth normal form is intended to decompose relation variables to irreducible components. Though this may be relatively unimportant for non-temporal relation variables, it can be important when dealing with temporal variables or other interval data. For instance, if a relation comprises a supplier's name, status, and city, we may also want to add temporal data, such as the time during which these values are, or were, valid (e.g., for historical data) but the three values may vary independently of each other and at different rates. We may, for instance, wish to trace the history of changes to Status; a review of production costs may reveal that a change was caused by a supplier changing city and hence what they charged for delivery.

For further discussion on Temporal Aggregation in SQL, see also Zimanyi.[7] For a different approach, see TSQL2.[8]

DKNF

Some authors have used the term sixth normal form differently: as a synonym for Domain/key normal form (DKNF). This usage predates Date et al.'s work. [9]

Usage

The sixth normal form is currently being used in some data warehouses where the benefits outweigh the drawbacks,[10] for example using Anchor Modeling. Although using 6NF leads to an explosion of tables, modern databases can prune the tables from select queries (using a process called 'table elimination') where they are not required and thus speed up queries that only access several attributes.

Examples

In order for a table to be in 6NF, it has to comply with the 5NF first and then it requires that each table satisfies only trivial join dependencies. Let’s take a simple example[11] with a table already in 5NF: Here, in the users table, every attribute is non null and the primary key is the username:

Users_table

Username	Department	Status

This table is in 5NF because each join dependency is implied by the unique candidate key of the table (Username). More specifically, the only possible join dependencies are: {username, status}, {username, department}.

The 6NF version would look like this:

Users

Username	Status

Users_dept

Username	Department

So, from one table in 5NF, 6NF produces two tables.

Following is another example:

TABLE 1

Medic Name	Occupation	Type	Practice in years
Smith James	orthopedic	specialist	23
Miller Michael	orthopedic	probationer	4
Thomas Linda	neurologist	probationer	5
Scott Nancy	orthopedic	resident	1
Allen Brian	neurologist	specialist	12
Turner Steven	ophthalmologist	probationer	3
Collins Kevin	ophthalmologist	specialist	7
King Donald	neurologist	resident	1
Harris Sarah	ophthalmologist	resident	2

The join dependencies of the table are {medic name, occupation}, {medic name, practice in years} and {medic name, type}. Hence we could see that such table is 2NF (due to the appearance of transitive dependency). The following tables try to bring it to 6NF:

TABLE 2.1

Medic Name	Occupation
Smith James	orthopedic
Miller Michael	orthopedic
Thomas Linda	neurologist
Scott Nancy	orthopedic
Allen Brian	neurologist
Turner Steven	ophthalmologist
Collins Kevin	ophthalmologist
King Donald	neurologist
Harris Sarah	ophthalmologist

TABLE 2.2

Medic Name	Practice in years
Smith James	23
Miller Michael	4
Thomas Linda	5
Scott Nancy	1
Allen Brian	12
Turner Steven	3
Collins Kevin	7
King Donald	1
Harris Sarah	2

TABLE 2.3

Medic Name	Type
Smith James	specialist
Miller Michael	probationer
Thomas Linda	probationer
Scott Nancy	resident
Allen Brian	specialist
Turner Steven	probationer
Collins Kevin	specialist
King Donald	resident
Harris Sarah	resident

References

1. Date, Darwen & Lorentzos 2003.
2. Date, Darwen & Lorentzos 2014.
3. Harrington 2009, pp. 125–126.
4. Date, Darwen & Lorentzos 2003, pp. 141–160.
5. Date, Darwen & Lorentzos 2003, p. 176.
6. Date, Darwen & Lorentzos 2014, p. 213.
7. Zimanyi 2006.
8. Snodgrass.
9. dbdebunk.
10. See the Anchor Modeling website for a website that describes a data warehouse modelling method based on the sixth normal form
11. Example provided by: http://www.anattatechnologies.com/q/2011/07/normalization-6nf/

Bibliography

• Date, Chris J.; Darwen, Hugh; Lorentzos, Nikos A. (January 2003). Temporal Data and the Relational Model: A Detailed Investigation into the Application of Interval and Relation Theory to the Problem of Temporal Database Management. Oxford: Elsevier LTD. ISBN 1-55860-855-9.CS1 maint: ref=harv (link)
• Date, Chris J.; Darwen, Hugh; Lorentzos, Nikos A. (12 August 2014). Time and relational theory - Temporal databases in the relational model and SQL. Elsevier-Morgan Kaufmann. ISBN 9780128006313.CS1 maint: ref=harv (link)
• Snodgrass, Richard T. "TSQL2 Temporal Query Language".CS1 maint: ref=harv (link)
• Zimanyi, E. (June 2006). "Temporal Aggregates and Temporal Universal Quantification in Standard SQL" (PDF). ACM SIGMOD Record, volume 35, number 2, page 16. ACM.CS1 maint: ref=harv (link)
• Date, Chris J. "ON DK/NF NORMAL FORM". Archived from the original on 6 April 2012.
• Harrington, Jan L. (2009). Relational Database Design and Implementation: Clearly Explained. Elsevier-Morgan Kaufmann. ISBN 9780123747303.CS1 maint: ref=harv (link)

Further reading

• Date, C.J. (2006). The relational database dictionary: a comprehensive glossary of relational terms and concepts, with illustrative examples. O'Reilly Series Pocket references. O'Reilly Media, Inc. p. 90. ISBN 978-0-596-52798-3.