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

From: Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be>
Date: Wed, 09 Mar 2005 08:21:34 GMT
Message-ID: <imyXd.33308\$mE4.3336247_at_phobos.telenet-ops.be>

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 DBMonster.com 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.

• Jan Hidders
Received on Wed Mar 09 2005 - 09:21:34 CET

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