# Re: completeness of the relational lattice

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

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

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