Re: SQL, related records (quotes)

From: Stefan Rybacki <stefan.rybacki_at_gmx.net>
Date: Sun, 26 Jun 2005 17:36:18 +0200
Message-ID: <3i80bkFk955oU1@individual.net>

Dan Guntermann wrote:
> "Stefan Rybacki" <stefan.rybacki_at_gmx.net> wrote in message
> news:3i78t2Fk4c3tU1_at_individual.net...
>

>>Dan Guntermann wrote:
>>
>>>...
>>>But alas, not many implementations allow for assertions of antisymmetry, 
>>>though it could be done with a trigger.  This approach would enforce the 
>>>condition that
>>>for all (child, parent) relationships that are members of hierarchies, 
>>>there does not exist a tuple of (parent, child).  It also has the 
>>>limiting factor of disallowing single node hierarchies.
>>
>>You meant non-symmetry since anti-symmetry says: you can have (child, 
>>parent) and (parent, child) at the same time execept parent=child

>
>
> Deesn't non-symmetry simply mean there exists a tuple <child X, parent Y> in
> hierarchies such that there is no corresponding tuple <child Y, parent X> in
> hierarchies? This isn't the same as a universal quantifier.
>
> No. I still think anti-symmetry in conjunction with non-reflexive holds
> here. Does the following meet the definition of anti-symmetry that you
> state above?

anti-symmetry + non-reflexifity = non-symmetry

Since anti-symmetry disallow symmetry except if both relation partners are equal. And non-reflexifity disallow this case a R a, so what remains is non-symmetry.

>
> child parent
> 6 3
> 3 6
>
> If it doesn't, then it makes sense that the DBMS reject such a condition.
> Obviously 6 does not equal 3.

Correct.

>
>

>>Just mentioned ;) (I know antisymmetry works here since you said you don't 
>>allow reflexive tupels)

>
>
> Right. Suppose a relation R on the domain A. For all a, b in the same
> domain A,
> a R b ^ b R a --> a = b, which is equivalent to
> ~(a R b ^ b R a) V a=b.

I know

>
> However, we have a constraint that asserts the condition a <> b. Thus, ~(a
> R b ^ b R a) V FALSE reduces to:
> ~(a R b ^ b R a).

Correct, this is exactly non-symmetry.

>
>

>>Regards
>>Stefan
>>
>>
>>>...

>
> Regards,
>
> Dan

Regards
Stefan

>
>
Received on Sun Jun 26 2005 - 10:36:18 CDT