Re: Question about Date & Darwen <OR> operator

Marshall Spight wrote:
> vc wrote:
> > Mikito Harakiri wrote:
> > >
> > > Let A be a relation with attributes x and y. Let B has attributes y and
> > > z. Then,
> > >
> > > A <OR> (A <AND> B) != A
> > >
> > > , since the header of A <AND> B has attributes x,y,z. There is no way
> > > the subsequent <OR> operation to reduce it to x,y.
> >
> > You are confused by mixing up the language and an interpretation. If
> > you consider A <OR> (A <AND> B) as a predicate formula, then the
> > identity holds. One can also claim that the identity holds for the
> > interpretation as well if one drops the column(s) representing an
> > entire attribute domain(s) from the result, very much in the same
> > fashion as when one added them to the original relations (your own
> > transformation).
>
> I don't believe A <OR> (A <AND> B) will have any columns representing
> an entire domain, unless A does already.

For the <AND> operation, A will be augmented with additional domains. Some tuples will be lost because of <AND>, but for the <OR> operation A will again be augmented with the same domains retained in their entirety thanks to the <OR> semantics. So I believe, the result can be stipped of the additional domains producing thus A unless I missed something in this exercise in combinatorics. Received on Tue Sep 06 2005 - 17:58:02 CEST