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join dependency : ウィキペディア英語版
join dependency
In the area of computer science known as dependency theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table T is subject to a join dependency if T can always be recreated by joining multiple tables each having a subset of the attributes of T. If one of the tables in the join has all the attributes of the table T, the join dependency is called trivial.
The join dependency plays an important role in the Fifth normal form, also known as ''project-join normal form'', because it can be proven that if you decompose a scheme R in tables R_1 to R_n, the decomposition will be a lossless-join decomposition if you restrict the legal relations on R to a join dependency on R called
*(R_1,R_2,\ldots,R_n).
Another way to describe a join dependency is to say that the set of relationships in the join dependency is independent of each other.
Unlike in the case of functional dependencies, there is no sound and complete axiomatization for join dependencies, though axiomatization exist for more expressive dependency languages such as full typed dependencies. However, implication of join dependencies is decidable.〔
== Formal definition ==

2-ary join dependencies are called multivalued dependency as a historical artifact of the fact that they were studied before the general case. More specifically if ''U'' is a set of attributes and ''R'' a relation over it, then ''R'' satisfies X \twoheadrightarrow Y if and only if ''R'' satisfies
*(X\cup Y, X\cup(U-Y)).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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