Transitive dependency

In mathematics, a transitive dependency is a functional dependency which holds by virtue of transitivity. A transitive dependency can occur only in a relation that has three or more attributes. Let A, B, and C designate three distinct attributes (or distinct collections of attributes) in the relation. Suppose all three of the following conditions hold:

# A → B
# It is not the case that B → A
# B → C

Then the functional dependency A → C (which follows from 1 and 3 by the axiom of transitivity) is a transitive dependency.

In database normalization, one of the important features of third normal form is that it excludes certain types of transitive dependencies. E.F. Codd, the inventor of the relational model, introduced the concepts of transitive dependence and third normal form in 1971.Codd, E.F. "Further Normalization of the Data Base Relational Model." (Presented at Courant Computer Science Symposia Series 6, "Data Base Systems," New York City, May 24th-25th, 1971.) IBM Research Report RJ909 (August 31st, 1971). Republished in Randall J. Rustin (ed.), "Data Base Systems: Courant Computer Science Symposia Series 6". Prentice-Hall, 1972. See pages 45-51, which cover third normal form and transitive dependence.]

Example

A transitive dependency occurs in the following relation:

The functional dependency {Book} → {Author Nationality} applies; that is, if we know the book, we know the author's nationality. Furthermore:

* {Book} → {Author}
* {Author} → {Author Nationality}
* {Author} does not → {Book}

Therefore {Book} → {Author Nationality} is a transitive dependency.

Notes