Re: completeness of the relational lattice

On Jun 29, 6:29 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 29 jun, 22:40, Jan Hidders <hidd..._at_gmail.com> wrote:
> > Sorry. The rules axiomatize the algebra for relations with finite
> > headers. When I redid parts of the completeness proof with the
> > corrected distribution rule new axioms for W kept on popping up, so I
> > decided to do the proof first without W. Once it's completely done I
> > might try to put it back in.
>
> I had a brief look and perhaps it's not so bad. It seems only the
> following rules are required for the introduction of W:
>
> (32a) W + [] = <>
> (32b) W + [x] = <x> with x a single attribute
> (55) W * <x> = W with x a single attribute
> (56) W + (r * s) = (W + r) * (W + s)

Challenge:

((W*P)+(W*Q))*W*R = (W*P*R)+(W*Q*R)

It could be proved if we know that A(W*P) = A(W*Q)= A(W*R)=A(W), or equivalently W*P*[]=W*Q*[]=W*R*[]=W*[] but how do we derive these? Received on Fri Jun 29 2007 - 21:54:02 CDT