Oracle FAQ | Your Portal to the Oracle Knowledge Grid |
Home -> Community -> Usenet -> comp.databases.theory -> Re: completeness of the relational lattice
On 29 jun, 22:40, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 29 jun, 18:20, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
>
> > On Jun 28, 3:41 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > > > I invite you to challenge me to show that it can prove an equation
> > > > > that holds. Of course you should also check if all these equations can
> > > > > be derived by you.
>
> > One more challenge:
>
> > <xy> + S + Q = <xy> + S
>
> > where S * [] = [z], and Q header is unconstrained. (I don't see axioms
> > about the lattice bottom element:-)
>
> 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)