Re: "Armstrong's axioms" augmentation - help plz

From: Jan Hidders <>
Date: Tue, 08 Mar 2005 20:51:41 GMT
Message-ID: <xfoXd.33031$>

paul c wrote:

> Dawn M. Wolthuis wrote:

>> "paul c" <toledobythesea_at_oohay.moc> wrote in message
>> news:n99Xd.599930$Xk.252349_at_pd7tw3no...
>>> Jan Hidders wrote:
>>>> love boat via wrote:
>>>>> I understand the Augmentation rule:
>>>>> { X -> Y } |= XZ -> YZ
>>>>> but I don't understand why the rule can also be stated as:
>>>>> { X -> Y } |= XZ -> Y
>>>>> Why is this?
>>>> It cannot. If you replace the first rule with the second you will 
>>>> not derive all FDs that hold.
>>> The first 'rule' is X -> Y, and so is the second!  What's the 
>>> difference?

>> The first rule implies the second as you pointed out, but the second
>> cannot stand in for the first as the implication goes only one
>> direction (from the first rule to the second and not from the second
>> statement of a rule to the first).
> are you really saying that before the answer can get smaller, it has to 
> get larger? (LOL)

Actually what Dawn was telling you is that if you want to get a bigger answer you need a rule that makes the answer bigger. Makes sense, no? The first rule allows you to do that, the second doesn't. Knowing that it's pretty simple to come up with a formal proof that you can derive less dependencies if you replace the first rule with the second one.

  • Jan Hidders
Received on Tue Mar 08 2005 - 21:51:41 CET

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