1977 AConsidrationOnNormalForm

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Subject Headings: Normalization, Normalized Database.


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2.1 Definition of relation

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



 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
1977 AConsidrationOnNormalFormAkifumi MakinouchiA Consideration on Normal Form of Not-Necessarily-Normalized Relation in the Relational Data ModelProceedings of the Third International Conference on Very Large Data Baseshttp://reference.kfupm.edu.sa/content/c/o/a consideration on normal form of not ne 465024.pdf1977