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

From: Jan Hidders <>
Date: Wed, 09 Mar 2005 08:21:34 GMT
Message-ID: <imyXd.33308$>

paul c wrote:

> Jan Hidders wrote:

>> 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.
> Looks like the answer IS getting bigger, based on the word count.

Not really. If in the set of FDs you start from the largest right-hand side has size n then you cannot derive an FD with a right-hand side that is larger than n.

Received on Wed Mar 09 2005 - 02:21:34 CST

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