Re: Universal Quantifier
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 27 Jan 2007 12:58:56 GMT
Message-ID: <k0Iuh.5748$1x.99929_at_ursa-nb00s0.nbnet.nb.ca>
>> On Jan 22, 11:02 am, "paul" <dm_ul..._at_yahoo.com> wrote:
>>
>>> Does someone know where I can learn more about Universal Quantifier
>>> (Predicate logica) in relation with Database design.
>>
>> Why not start here:
>>
>> http://en.wikipedia.org/wiki/Universal_quantification
>>
>> Always fun to spend an evening chasing Wikipedia links. At least
>> until you end up at an article about a metal band.
>>
>> Consider that database constraints can be expressed as quantified
>> logical formula. If table A has primary key p and table B has attribute
>> q which is a foreign key referencing A(p), we could express that as:
>>
>> forall B(q). exists A(p). p=q;
>> ...
>
> What formula would express a primary key?
Date: Sat, 27 Jan 2007 12:58:56 GMT
Message-ID: <k0Iuh.5748$1x.99929_at_ursa-nb00s0.nbnet.nb.ca>
paul c wrote:
> Marshall wrote: >
>> On Jan 22, 11:02 am, "paul" <dm_ul..._at_yahoo.com> wrote:
>>
>>> Does someone know where I can learn more about Universal Quantifier
>>> (Predicate logica) in relation with Database design.
>>
>> Why not start here:
>>
>> http://en.wikipedia.org/wiki/Universal_quantification
>>
>> Always fun to spend an evening chasing Wikipedia links. At least
>> until you end up at an article about a metal band.
>>
>> Consider that database constraints can be expressed as quantified
>> logical formula. If table A has primary key p and table B has attribute
>> q which is a foreign key referencing A(p), we could express that as:
>>
>> forall B(q). exists A(p). p=q;
>> ...
>
> 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.