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Fourth normal form and Multi-valued dependencies

 

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

 

Pizza varieties offered by a restaurant are not affected by delivery area (i.e. a restaurant offers all pizza varieties it makes to all areas it supplies), 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} ↠ {\displaystyle \twoheadrightarrow } \twoheadrightarrow {Pizza Variety}
  • {Restaurant} ↠ {\displaystyle \twoheadrightarrow } \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.

References:

https://en.wikipedia.org/wiki/Fourth_normal_form#Multivalued_dependencies