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Re: armstrong's axioms: augmentation - help pls

From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Fri, 03 Dec 2004 18:36:03 GMT
Message-ID: <nm2sd.8939$g94.550005@phobos.telenet-ops.be>


loveboat wrote:
> hi,
>
> in armstrongs axioms, i don't get the augmentation, which is:
> (X -> Y) => (XZ -> YZ)
>
> why is that? i mean when Y is functional depending from X, i can't just add
> another set of attributes and make them dependent as well? (at least that's
> what i think)
> why can i do that?

That's actually quite simple. Try a concrete example. Suppose that X = "name" and Y = "age", then the dependency X -> Y means that if I give you a name then there is only one corresponding age. Let's assume for example that "Fred" has age 27 and Mary has age 29.

If Z = "job" then XZ -> YZ means that for every pair of name and job that I give you there is only one corresponding pair of age and job. This is rather obvious because if I give you the combination "Fred" and "secretary" then you know that there is a unique corresponding pair "27" and "secretary"; the first part ("27") is unique because that is determined by the value "Fred" and the second part is unique because it can only be the value "secretary" that was already given in the first pair.

See?

Received on Fri Dec 03 2004 - 12:36:03 CST

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