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"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?
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.
>
> 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.
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).
>
> Regards
> Stefan
>
> >...
Regards,
Dan Received on Sun Jun 26 2005 - 06:38:13 CDT