# Re: completeness of the relational lattice

Date: Fri, 22 Jun 2007 12:11:23 -0700

Message-ID: <1182539483.277381.122090_at_x35g2000prf.googlegroups.com>

On Jun 22, 11:20 am, Jan Hidders <hidd..._at_gmail.com> wrote:

> On 22 jun, 19:36, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:

*>
**> > On Jun 22, 3:08 am, Jan Hidders <hidd..._at_gmail.com> wrote:
**>
**> > > > > We cannot distribute in general, but we have a specific distribution rule:
**>
**> > > > > (1) r /\ ((s \/ [H]) \/ (t\/[H])) = r /\ (s \/ [H]) \/ r*(t \/ [H])
**>
**> > > > Which is BTW a very limited case embraced by Spight criteria.
**>
**> > > Indeed. But it is a simple equation, no premises.
**>
**> > Your premise is that H is a set of attributes which is a subset of
**> > attributes of relations s and t
**>
**> No, any set of attributes H will do.
*

Counterexample:

r(x,y) = {(1,7),(1,4),(2,4),(2,7)} s(x) = {2} t(y) = {7}

H = {x,y}

s \/ [H] = {2}

t \/ [H] = {7}

((s \/ [H]) \/ (t\/[H])) = 01

r /\ ((s \/ [H]) \/ (t\/[H])) = *** {(1,7),(1,4),(2,4),(2,7)} *** r /\ (s \/ [H]) = {(2,4),(2,7)} r /\ (t \/ [H]) = {(1,7),(2,7)} r /\ (s \/ [H]) \/ r*(t \/ [H]) = *** {(1,7),(2,4),(2,7)} ***

Anyway, let follow Marshall suggestion and move along to axioms. Received on Fri Jun 22 2007 - 21:11:23 CEST