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 ${\displaystyle R}$ in tables ${\displaystyle R_{1}}$ to ${\displaystyle R_{n}}$, the decomposition will be a lossless-join decomposition if you restrict the legal relations on ${\displaystyle R}$ to a join dependency on ${\displaystyle R}$ called ${\displaystyle *(R_{1},R_{2},\ldots ,R_{n})}$.

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