Re: Universal Quantifier

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 27 Jan 2007 23:08:13 GMT
Message-ID: <xXQuh.5999$1x.103474@ursa-nb00s0.nbnet.nb.ca>

paul c wrote:

> Bob Badour wrote:
>

>> paul c wrote:
>>
>>> Bob Badour wrote:
>>>
>>>> ...
>>>>
>>>>> What formula would express a primary key?
>>>>
>>>> Faking it heavily, I suggest something along the lines of:
>>>>
>>>> forall A1(p1,q1) in A(p,q). forall A2(p2,q2) in A(p,q).
>>>>   if p1 = p2 then q1 = q2;
>>>>
>>>> where p is actually the set of attributes composing the key and q is 
>>>> actually the set of dependent attributes.
>>>>
>>>> One also has to express irreducibility, though.
>>>
>>> Regarding irreducibility, do we not express it by our choice of p1 and
>>> p2?  Ie., what we express with a reducible p1 is extraneous?
>>
>> But one can still express that using not exists and some proper subset 
>> of P.

>
> I think I see what you mean, will try to write it for myself - it does
> seem nice and precise to be able to say what property the irreducible
> set is by saying that a "proper" superset of it is reducible, assuming
> that's what you mean. Also would feel nice somehow, at least to me, if
> we could express table_dee and dum that way too, just trying to dot some
> i's.

That's what reducible means. If a key is reducible, some proper subset of its attributes is also a key. To say that a candidate key is irreducible simply means no such proper subset exhibits the necessary property.

The formulae we discussed earlier express that P is a superkey. The other requirement for a candidate key is irreducibility.

The proof would hold for DEE and DUM because no proper subset of any of their attributes exists. Received on Sat Jan 27 2007 - 17:08:13 CST