Re: Distributivity in Tropashko's Lattice Algebra

Mikito Harakiri wrote:
> VC wrote:
> > "Mikito Harakiri" <mikharakiri_nospaum_at_yahoo.com> wrote in message
> > news:1124225375.601615.162210_at_g47g2000cwa.googlegroups.com...
> > >
> > > vc wrote:
> > >> A union '00' = '00'.
> > >
> > > This can't be.
> > >
> > > A union '00' = '00'
> > >
> > > implies 00 < A, and the partial order "<" being the same in upper and
> > > lower semilattice implies that
> > >
> > > A join '00' = A
> > >
> > > which we saw isn't.
> > >
> >
> > OK, apparently your definition of '00' is different from mine. What
> > relation does '00' stand for ?
>
> Informally, 00 is a relation with 0 attributes and 0 rows. Apparently,
> it's not easy to define it in lattice terms.
>
>
> There is another argument against
>
> A union 00 = 00
>
> For any two relations A and B, the relation
>
> A union B
>
> has cardinality bigger than both A and B. In you proposition this
> property is lost.

Extending your idea further it is tempting to define

A union B = 00

whenever A and B have a disjoint set of attributes. A union B is certainly a relation with empty header. It's cardinality can't be 0, however, as it would result in inconsistency. Received on Wed Aug 17 2005 - 20:01:23 CEST