Re: thinking about UPDATE

From: D Guntermann <guntermann_at_hotmail.com>
Date: Fri, 23 Jul 2004 01:43:23 GMT
Message-ID: <I1A7GB.Evo@news.boeing.com>

"Mikito Harakiri" <mikharakiri_at_iahu.com> wrote in message news:vqZLc.61$X73.405_at_news.oracle.com...
> "D Guntermann" <guntermann_at_hotmail.com> wrote in message
> news:I1A396.CB5_at_news.boeing.com...
> >
> > "Mikito Harakiri" <mikharakiri_at_iahu.com> wrote in message
> > news:QiXLc.58$X73.394_at_news.oracle.com...
> > >
> > > "D Guntermann" <guntermann_at_hotmail.com> wrote in message
> > > news:I19vBu.41M_at_news.boeing.com...
> > > > I might be missing something here, but can one have a relation
> variable
> > > > extensionally defined with one or more attributes where the key is
the
> > > empty
> > > > set?
> > >
> > > Without loss of generality we can limit our scope to FDs with RHS set
> > > containing one column only. Then,
> > >
> > > {} -> {A.X}
> > >
> > > means
> > >
> > > not exists a1,a2 ( a1.x != a2.x )
> > >
> > > Since this is true for any column X, then it simply says "no duplicate
> a1
> > > and a2 are allowed" -- a relation with one tuple, at most.

>

> There was a typo there: "only duplicate a1 and a2 are allowed"

>


> > Perfectly understood!  Thanks Mikito.  Now, a follow-up:

> >

> > From {} -> {A.X} above, we could get: {} -> {{},A.X}.

> >

> > What are the implications of this?

> >
> > Would your predicate logic still hold?
>
> This is really what "Without loss of generality" disclaimer took care of.
On
> FDs Right Hand Side you can have any number of columns, but all these
cases
> are trivial generalizations of the "canonic" case when you have only one
> column. Indeed,

But what is the domain of {{}.{},A.X}}(i.e. a listing of valid tuple values)? Is it not {}? Thus, not even one value of A.X should exist.

If the empty set shouldn't be allowed on the RHS, then how is it allowed as a proper subset using the rules of deriving functional dependencies? It must come from a superset on the LHS in the first place, right?

>

> {X,Y} -> {U}

>

> and

>

> {X,Y} -> {V}

>

> imply

>

> {X,Y} -> {U,V}

>

> therefore, sets on the right side don't really buy us something.

>

> (Aside from the simple fact, that allowing sets in place of columns is
> formally illegal in classic dependency theory).

Well, I think this is what I am getting at, ultimately. Something really bothers me about the use of the empty set in FD's. I can't quite place my finger on it, but it seems inconsistent by some rules and definitions.

Thanks for the response.

Regards,

Dan

>
>
>

Received on Thu Jul 22 2004 - 20:43:23 CDT