# 1977 AConsidrationOnNormalForm

- (Makinouchi, 1977) ⇒ Akifumi Makinouchi. (1977). “A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model.” In: Proceedings of the Third International Conference on Very Large Data Bases (VLDB 1977).

**Subject Headings:** Normalization, Normalized Database.

## Notes

- It defines a Relation and a Relational Table.

## Cited By

## Quotes

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### 2.1 Definition of relation

Mathematically, a relation is defined as follows: Given sets [math]\displaystyle{ D_1, D_2, ..., D_n }[/math], (not necessarily distinct), [math]\displaystyle{ R }[/math] is a relation on these [math]\displaystyle{ n }[/math] sets if it is a set of n-tuples ([math]\displaystyle{ d_1, d_2, ..., d_n }[/math]) such that [math]\displaystyle{ d_i }[/math] belongs to [math]\displaystyle{ D_i }[/math], where [math]\displaystyle{ i=l, 2, ..., n }[/math]. [math]\displaystyle{ D_1, D_2, ..., D_n }[/math] are domains of [math]\displaystyle{ R }[/math].

In the realm of relational data model, a relation as above looks like a table (array) each of whose columns has different names. In the sequel, we use tables and relations interchangeably, but domains and columns differently. Each column name of a relation represents a role name in the relation and its domain is a set of values which may possibly be inserted into the column. Each row of the relation consists of an n-tuple of values.

When the domain of every column of a relation is a set of such values that they can be represented by an integer, a character string, etc., we call it a normalized relation. Such a value is said to be atomic and a column whose domain is a set of atomic values is called an atomic column.

To admit not-flat tables, we allow the domain of columns of a relation to be a set of sets. More precisely, a domain may be a Potenzmenge* [9] or power set of another relation.

We call such a column a relation column to differentiate from atomic columns, and such an embedded relation a dependent relation to distinguish it from an independent relation (not embedded in any other relation).

In Fig. 1, an example of unnormalized relation UN-EMP and the corresponding normalized relating N-EMP are shown. For the sake of makinq distinction, a column name of embedded relation is modified with the relation name on normalization.

A row and column position of an unnormalized relation contains a set of tuples when the column is a relation column. For example, a tuple of the relation UN-EMP in Fig. 1, (69001, {ICHIRO, HANAKO], {(1975,lOOOO),(1976, llOOO)]) indicates that an employee whose employee number is 69001 has two children to support named ICHIRO and HANAKO respectively, and earned $10,000 in 1975 and $11,000 in 1976. Since the objective of this paper is to introduce such a new normal form on unnormalized relation that storage operation anomalies could be avoided just as the 3NF of Codd could, adequate definitions must be carefully chosen from many possible ones.

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Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
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1977 AConsidrationOnNormalForm | Akifumi Makinouchi | A Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data Model | http://reference.kfupm.edu.sa/content/c/o/a consideration on normal form of not ne 465024.pdf |