Re: A simple notation, again

From: paul c <>
Date: Tue, 17 Jul 2007 13:51:49 GMT
Message-ID: <VP3ni.126636$1i1.122622_at_pd7urf3no>

Brian Selzer wrote:
> "paul c" <> wrote in message
> news:4kWmi.125098$1i1.56624_at_pd7urf3no...

>>Also, this gives me an excuse to mention one of my pet penchants again. 
>><NOT> (A <OR> B) is the complement of a union in D&D terms and when A <OR> 
>>B is true, it implies that (<NOT> A) <AND> (<NOT> B) is false.  I find it 
>>interesting to think about a relation's complement when thinking about 
>>insert to "union".  When A and B have the same heading and we insert a 
>>single tuple to a view that is A <OR> B, some people say inserting to one 
>>or the other of A or B is just as logical as inserting to both A and B, so 
>>we can't really decide what to do.  But it seems reasonable to me that the 
>>complement of the view must also respect the complements of A and B, so 
>>neither of those complements should contain the inserted tuple, which 
>>means that both A and B would contain it after the insert.

> I don't think this is quite right.
> Suppose t is a tuple whose presence in A or in B would not violate any
> constraints. Then t must necessarily be an element of either A or its
> complement, and t must necessarily be an element of either B or its
> compliment. Now, if t does not appear in A union B, then t must necessarily
> be an element of both the complement of A and the complement of B. As a
> result, an insert of t into the view, A union B, does not map to any one of
> these operations: (1) an insert of t into A, (2) an insert of t into B, or
> (3) an insert of t into both A and B.
> ...

I mentioned "insert ... to a view" but I think I shouldn't have, because dbms's don't insert into views!


> As an aside: if one adheres to the Principle of Orthogonal Design, then the
> individual represented by the tuple t can never* exemplify both A and
> B--that is, t would violate the predicate of A or of B, so an insert of t
> into the view, A union B, would necessarily be deterministic. (There is one
> exception, but it is trivial: when the keys of both A and B are composed of
> their entire headings and when an inclusion dependency is defined between A
> and B, then it is possible for t to exemplify both A and B, but it should be
> obvious that the view, A union B, would necessarily be composed of just
> those tuples that exist in whichever is the referenced relation, so it would
> be pointless to create such a view in the first place.)


Received on Tue Jul 17 2007 - 15:51:49 CEST

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