Re: Foreign keys

From: Jan Hidders <>
Date: Wed, 16 Jan 2008 14:37:02 -0800 (PST)
Message-ID: <>

On 15 jan, 08:24, Kira Yamato <> wrote:
> On 2008-01-14 21:18:57 -0500, "Evan Keel" <> 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 attributes.
> 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?

Not really. Your observation that sometimes the inference rules are the same for functional and inclusion dependencies is correct, but unfortunately this is not true in general. For example, the augmentation rule does not always hold for inclusion dependencies. In fact, axiomatizing the combination of functional and inclusion dependencies is a notoriously difficult problem and in the past there has been intensive research on that subject.

  • Jan Hidders

> --
> -kira
Received on Wed Jan 16 2008 - 23:37:02 CET

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