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Fourth normal form (4NF) is a normal form used in database normalization. Introduced by Ronald Fagin in 1977, 4NF is the next level of normalization after Boyce–Codd normal form (BCNF). Whereas the second, third, and Boyce–Codd normal forms are concerned with functional dependencies, 4NF is concerned with a more general type of dependency known as a multivalued dependency. A Table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies X $\twoheadrightarrow$ Y, X is a superkey—that is, X is either a candidate key or a superset thereof.^[1]

Multivalued dependencies

If the column headings in a relational database table are divided into three disjoint groupings X, Y, and Z, then, in the context of a particular row, we can refer to the data beneath each group of headings as x, y, and z respectively. A multivalued dependency X $\twoheadrightarrow$ Y signifies that if we choose any x actually occurring in the table (call this choice x_c), and compile a list of all the x_cyz combinations that occur in the table, we will find that x_c is associated with the same y entries regardless of z.

A trivial multivalued dependency X $\twoheadrightarrow$ Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation.

A functional dependency is a special case of multivalued dependency. In a functional dependency X → Y, every x determines exactly one y, never more than one.

Example

Consider the following example:

Pizza Delivery Permutations
Restaurant	Pizza Variety	Delivery Area
A1 Pizza	Thick Crust	Springfield
A1 Pizza	Thick Crust	Shelbyville
A1 Pizza	Thick Crust	Capital City
A1 Pizza	Stuffed Crust	Springfield
A1 Pizza	Stuffed Crust	Shelbyville
A1 Pizza	Stuffed Crust	Capital City
Elite Pizza	Thin Crust	Capital City
Elite Pizza	Stuffed Crust	Capital City
Vincenzo's Pizza	Thick Crust	Springfield
Vincenzo's Pizza	Thick Crust	Shelbyville
Vincenzo's Pizza	Thin Crust	Springfield
Vincenzo's Pizza	Thin Crust	Shelbyville

Each row indicates that a given restaurant can deliver a given variety of pizza to a given area.

The table has no non-key attributes because its only key is {Restaurant, Pizza Variety, Delivery Area}. Therefore it meets all normal forms up to BCNF. If we assume, however, that pizza varieties offered by a restaurant are not affected by delivery area, then it does not meet 4NF. The problem is that the table features two non-trivial multivalued dependencies on the {Restaurant} attribute (which is not a superkey). The dependencies are:

{Restaurant} $\twoheadrightarrow$ {Pizza Variety}
{Restaurant} $\twoheadrightarrow$ {Delivery Area}

These non-trivial multivalued dependencies on a non-superkey reflect the fact that the varieties of pizza a restaurant offers are independent from the areas to which the restaurant delivers. This state of affairs leads to redundancy in the table: for example, we are told three times that A1 Pizza offers Stuffed Crust, and if A1 Pizza starts producing Cheese Crust pizzas then we will need to add multiple rows, one for each of A1 Pizza's delivery areas. There is, moreover, nothing to prevent us from doing this incorrectly: we might add Cheese Crust rows for all but one of A1 Pizza's delivery areas, thereby failing to respect the multivalued dependency {Restaurant} $\twoheadrightarrow$ {Pizza Variety}.

To eliminate the possibility of these anomalies, we must place the facts about varieties offered into a different table from the facts about delivery areas, yielding two tables that are both in 4NF:

Varieties By Restaurant
Restaurant	Pizza Variety
A1 Pizza	Thick Crust
A1 Pizza	Stuffed Crust
Elite Pizza	Thin Crust
Elite Pizza	Stuffed Crust
Vincenzo's Pizza	Thick Crust
Vincenzo's Pizza	Thin Crust

Delivery Areas By Restaurant
Restaurant	Delivery Area
A1 Pizza	Springfield
A1 Pizza	Shelbyville
A1 Pizza	Capital City
Elite Pizza	Capital City
Vincenzo's Pizza	Springfield
Vincenzo's Pizza	Shelbyville

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In contrast, if the pizza varieties offered by a restaurant sometimes did legitimately vary from one delivery area to another, the original three-column table would satisfy 4NF.

Ronald Fagin demonstrated that it is always possible to achieve 4NF.^[2] Rissanen's theorem is also applicable on multivalued dependencies.

4NF in practice

A 1992 paper by Margaret S. Wu notes that the teaching of database normalization typically stops short of 4NF, perhaps because of a belief that tables violating 4NF (but meeting all lower normal forms) are rarely encountered in business applications. This belief may not be accurate, however. Wu reports that in a study of forty organizational databases, over 20% contained one or more tables that violated 4NF while meeting all lower normal forms.^[3]

References

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↑ "A relation schema R* is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency X $\twoheadrightarrow$ Y holds for R*, then so does the functional dependency X → A for every column name A of R*. Intuitively all dependencies are the result of keys." One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Fagin, p. 268
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[Fagin-1] "A relation schema R* is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency X $\twoheadrightarrow$ Y holds for R*, then so does the functional dependency X → A for every column name A of R*. Intuitively all dependencies are the result of keys." One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[Fagin268-2] Fagin, p. 268

[Wu-3] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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+'''Fourth normal form''' ('''4NF''') is a [[Database normalization#Normal forms|normal form]] used in [[database normalization]]. Introduced by [[Ronald Fagin]] in 1977, 4NF is the next level of normalization after [[Boyce–Codd normal form]] (BCNF). Whereas the [[Second normal form|second]], [[Third normal form|third]], and [[Boyce–Codd normal form|Boyce–Codd]] normal forms are concerned with [[functional dependency|functional dependencies]], 4NF is concerned with a more general type of dependency known as a [[multivalued dependency]]. A [[Table (database)|Table]] is in 4NF [[if and only if]], for every one of its non-trivial multivalued dependencies ''X'' <math>\twoheadrightarrow</math> ''Y'', ''X'' is a [[superkey]]—that is, ''X'' is either a [[candidate key]] or a superset thereof.<ref name="Fagin">"A relation schema R* is in fourth normal form (4NF) if, whenever a nontrivial multivalued dependency X <math>\twoheadrightarrow</math> Y holds for R*, then so does the functional dependency X → A for every column name A of R*. Intuitively all dependencies are the result of keys." {{cite journal|first=Ronald|last=Fagin|title=Multivalued Dependencies and a New Normal Form for Relational Databases|journal=ACM Transactions on Database Systems|volume=2|issue=1|date=September 1977|pages=267|url=http://www.almaden.ibm.com/cs/people/fagin/tods77.pdf|doi=10.1145/320557.320571}}</ref>
+==Multivalued dependencies==
+If the column headings in a relational database table are divided into three disjoint groupings ''X'', ''Y'', and ''Z'', then, in the context of a particular row, we can refer to the data beneath each group of headings as ''x'', ''y'', and ''z'' respectively. A [[multivalued dependency]] ''X'' <math>\twoheadrightarrow</math> ''Y'' signifies that if we choose any ''x'' actually occurring in the table (call this choice ''x<sub>c</sub>''), and compile a list of all the ''x<sub>c</sub>yz'' combinations that occur in the table, we will find that ''x<sub>c</sub>'' is associated with the same ''y'' entries regardless of z.
+A '''trivial multivalued dependency''' ''X'' <math>\twoheadrightarrow</math> ''Y'' is one where either ''Y'' is a subset of ''X'', or ''X'' and ''Y'' together form the whole set of attributes of the relation.
+A [[functional dependency]] is a special case of multivalued dependency. In a functional dependency ''X'' → ''Y'', every ''x'' determines ''exactly one y'', never more than one.
+==Example==
+Consider the following example:
+{| class="wikitable"
+|+ Pizza Delivery Permutations
+! <u>Restaurant</u> !! <u>Pizza Variety</u> !! <u>Delivery Area</u>
+|-
+|A1 Pizza||Thick Crust||Springfield
+|-
+|A1 Pizza||Thick Crust||Shelbyville
+|-
+|A1 Pizza||Thick Crust||Capital City
+|-
+|A1 Pizza||Stuffed Crust||Springfield
+|-
+|A1 Pizza||Stuffed Crust||Shelbyville
+|-
+|A1 Pizza||Stuffed Crust||Capital City
+|-
+|Elite Pizza||Thin Crust||Capital City
+|-
+|Elite Pizza||Stuffed Crust||Capital City
+|-
+|Vincenzo's Pizza||Thick Crust||Springfield
+|-
+|Vincenzo's Pizza||Thick Crust||Shelbyville
+|-
+|Vincenzo's Pizza||Thin Crust||Springfield
+|-
+|Vincenzo's Pizza||Thin Crust||Shelbyville
+|}
+Each row indicates that a given restaurant can deliver a given variety of pizza to a given area.
+The table has no non-key attributes because its only key is {Restaurant, Pizza Variety, Delivery Area}. Therefore it meets all normal forms up to BCNF. If we assume, however, that pizza varieties offered by a restaurant are not affected by delivery area, then it does not meet 4NF. The problem is that the table features two non-trivial multivalued dependencies on the {Restaurant} attribute (which is not a superkey). The dependencies are:
+* {Restaurant} <math>\twoheadrightarrow</math> {Pizza Variety}
+* {Restaurant} <math>\twoheadrightarrow</math> {Delivery Area}
+These non-trivial multivalued dependencies on a non-superkey reflect the fact that the varieties of pizza a restaurant offers are independent from the areas to which the restaurant delivers. This state of affairs leads to [[Data redundancy|redundancy]] in the table: for example, we are told three times that A1 Pizza offers Stuffed Crust, and if A1 Pizza starts producing Cheese Crust pizzas then we will need to add multiple rows, one for each of A1 Pizza's delivery areas. There is, moreover, nothing to prevent us from doing this incorrectly: we might add Cheese Crust rows for all but one of A1 Pizza's delivery areas, thereby failing to respect the multivalued dependency {Restaurant} <math>\twoheadrightarrow</math> {Pizza Variety}.
+To eliminate the possibility of these anomalies, we must place the facts about varieties offered into a different table from the facts about delivery areas, yielding two tables that are both in 4NF:
+{| class="wikitable" style="margin: 10px; float:left;"
+|+ Varieties By Restaurant
+! <u>Restaurant</u> !! <u>Pizza Variety</u>
+|-
+|A1 Pizza||Thick Crust
+|-
+|A1 Pizza||Stuffed Crust
+|-
+|Elite Pizza||Thin Crust
+|-
+|Elite Pizza||Stuffed Crust
+|-
+|Vincenzo's Pizza||Thick Crust
+|-
+|Vincenzo's Pizza||Thin Crust
+|}
+{| class="wikitable" style="margin: 10px; float:left;"
+|+ Delivery Areas By Restaurant
+! <u>Restaurant</u> !! <u>Delivery Area</u>
+|-
+|A1 Pizza||Springfield
+|-
+|A1 Pizza||Shelbyville
+|-
+|A1 Pizza||Capital City
+|-
+|Elite Pizza||Capital City
+|-
+|Vincenzo's Pizza||Springfield
+|-
+|Vincenzo's Pizza||Shelbyville
+|}
+{{-}}
+In contrast, if the pizza varieties offered by a restaurant sometimes did legitimately vary from one delivery area to another, the original three-column table would satisfy 4NF.
+Ronald Fagin demonstrated that it is always possible to achieve 4NF.<ref name="Fagin268">Fagin, p. 268</ref> [[Rissanen's theorem]] is also applicable on [[Multivalued dependency|multivalued dependencies]].
+==4NF in practice==
+A 1992 paper by Margaret S. Wu notes that the teaching of database normalization typically stops short of 4NF, perhaps because of a belief that tables violating 4NF (but meeting all lower normal forms) are rarely encountered in business applications. This belief may not be accurate, however. Wu reports that in a study of forty organizational databases, over 20% contained one or more tables that violated 4NF while meeting all lower normal forms.<ref name="Wu">{{cite journal|first=Margaret S.|last=Wu|title=The Practical Need for Fourth Normal Form|journal=ACM SIGCSE Bulletin|volume=24|issue=1|date=March 1992|pages=19–23|doi=10.1145/135250.134515}}</ref>
+==See also==
+*[[Attribute-value system]]
+<!-- See navigation box at bottom of page. -->
+==References==
+{{Reflist}}
+==Further reading==
+{{Refbegin}}
+*Date, C. J. (1999), ''[http://www.aw-bc.com/catalog/academic/product/0,1144,0321197844,00.html An Introduction to Database Systems]'' (8th ed.). Addison-Wesley Longman. ISBN 0-321-19784-4.
+*Kent, W. (1983) ''[http://www.bkent.net/Doc/simple5.htm A Simple Guide to Five Normal Forms in Relational Database Theory]'', Communications of the ACM, vol. 26, pp.&nbsp;120–125
+*[http://www.utexas.edu/its/windows/database/datamodeling/rm/rm8.html Advanced Normalization] by ITS, University of Texas.
+{{Refend}}
+{{Database normalization}}
+[[Category:Database normalization|4NF]]
+[[de:Normalisierung (Datenbank)#Vierte Normalform (4NF)]]

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4NF in practice

See also

References

Further reading

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