# 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>

>>> Dawn M. Wolthuis wrote:

>

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

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