# Re: SQL, related records (quotes)

Date: Sun, 26 Jun 2005 17:36:18 +0200

Message-ID: <3i80bkFk955oU1_at_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 - 17:36:18 CEST