In the Russian-language and English-language articles about the third normal form of the relationship are very strange formulations of transitive functional dependency.

(The relation is in the third normal form, if it is in the second, and there is no transitive functional relationship between the potential key and the non-key attribute)

Russian-language Wikipedia: the functional dependence X → Z is transitive if there is a Y such that X → Y → Z, and none of the functional dependencies X → Y, Y → Z, X → Z is trivial. You can choose one potential key as X, another potential key as Y, which is not contained in X, and any non-key attribute as Z. However, the simplest cases of such relations should be in 3NF according to the alternative definition of Carlo Zaniolo.

(An alternative definition of Carlo Zaniolo is that for any functional dependence of the form X → {A} at least one of three conditions is true: X is a superkey, A lies in X, A is a key attribute.)

English-language Wikipedia: the functional relationship X → Z is transitive if there is a Y such that X → Y → Z, all X, Y, Z are different, and Y → X is not satisfied. Closer to the truth, but you can still take as X a potential key, as Y the set of two non-key attributes, and as Z a singleton subset of Y.

Would it not be reasonable to replace the condition of the inequality X, Y, Z by the condition that the functional dependence Y → Z? Is non-trivial? Then everything will be in agreement with Carlo Zaniolo.

    1 answer 1

    Would it not be reasonable to replace the condition of the inequality X, Y, Z by the condition that the functional dependence Y → Z? Is non-trivial? Then everything will be in agreement with Carlo Zaniolo.

    No, since in this case there remains the possibility of the existence of a trivial functional dependence X → Y, and the condition from the English-language article "all X, Y, Z are different" and from the Russian-language article ... ... and none of the functional dependencies X → Y, Y → Z, X → Z is not trivial "this is prohibited.

    • Why does the pairwise inequality X, Y, Z forbid the triviality X → Y? However, current formulations also lead to incidents and incompatibilities with alternative definitions. Is there any more reliable source? It would seem that there is nothing wrong with the triviality of X → Y; nevertheless, some simplification of the functional dependency from a potential key to some smaller subset of its attributes, that is, we should want to normalize it. - Akari Gale
    • Well, in the proof of equivalence it is clear that exactly these two properties are required (the absence of Y → X and the non-triviality of Y → Z). Maybe then it is generally not necessary to formulate the definition of a third normal form in terms of transitivity? - Akari Gale
    • @AkariGale is just a detailed explanation for the possibility of transitive dependence in principle. Since if we allow the triviality of X -> Y, then by the definition of a trivial functional dependence we get a situation not such that X -> Y, Y -> Z, X -> Z, but a completely different one. Those. X -> Y can be viewed as just X (Y as a subset of the determinant X, it will be “absorbed”) and the expression takes the form: X -> Z, which in turn is not transitive by definition. - edem
    • I agree. However, it still turns out that the English definition of transitive dependence does not prohibit it? For X and Y are just different. - Akari Gale
    • It turns out that this aspect is not relevant in determining the third normal form, since this situation is blocked at the level of the second normal form. Therefore, can we put the final definition X → Y and Y → Z non-trivial, Y → X wrong? This preserves equivalence and gives an acceptable form of transitive dependence - Akari Gale