Re: Foreign keys
Date: Tue, 15 Jan 2008 04:37:23 -0500
"Kira Yamato" <kirakun_at_earthlink.net> wrote in message
> On 2008-01-14 21:18:57 -0500, "Evan Keel" <evankeel_at_sbcglobal.net> said:
>> Always a physical issue. Never a theory issue.Agree?
> Foreign keys are functional dependencies across two relations.
> More specifically, let
> R1(K1, A1, B1)
> be a relation with attribute sets K1, A1 and B1 where K1 is R1's primary
> key and B1 is a foreign key to the relation
> R2(K2, A2)
> where K2 is R2's primary key and A2 is the set of its remaining
> Then the foreign key B1 represents the functional dependency
> B1 --> A2,
> which is the functional dependency across two relation I mentioned in the
> first sentence.
> Furthermore, through transitivity by the functional dependency K1 --> B1,
> the foreign key also represents the inter-relational functional dependency
> K1 --> A2.
> Am I correct to say this?
I don't think so. A functional dependency A --> B is surjective, meaning not only that for every A there must be one and only one B, but also that for every B there must be at least one A. The relationship between B1 and A2 above is injective, as is the relationship between K1 and A2.
Received on Tue Jan 15 2008 - 10:37:23 CET