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_at_ursa-nb00s0.nbnet.nb.ca>
>
> 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.
Date: Sat, 27 Jan 2007 23:08:13 GMT
Message-ID: <xXQuh.5999$1x.103474_at_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 Sun Jan 28 2007 - 00:08:13 CET