Re: completeness of the relational lattice

On 26 jun, 19:55, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:

>
>
> OK now you earned your notation. If you also derive (R /\ 00) \/ (R /\
> 11) = R, I would be totally sold out.

I hope you'll forgive me if I'm slightly skeptical about that. :-) Anyway, such a challenge I cannot refuse, of course. To be clear, I will answer the points you raised, but that requires some more thinking, because there are some deep and fundamental issues there, and that requires some more thought.

So you want me to prove, in my notation:

  (R(x,y) * []) + (R(x,y) * W) = R(x,y)

Ready! ... Set! ... Go!

          (R(x,y) * []) + (R(x,y) * W)
(22) = [x,y] + (R(x,y) * W)
(9) = ([x,y] + R(x,y)) * ([x,y] + W)
(10) = R(x,y) * ([x,y] + W)
(11) = R(x,y) * (([x] * [y]) + W)
(9) = R(x,y) * (([x] + W) * ([y] + W))
(32b) = R(x,y) * <x> * <y>
(28) = R(x,y)

Remark: rule 32b is from the posting with errata for the rules for W. To repeat:

(32a) W + [] = {()}
(32b) W + [x] = <x> with x a single attribute
(32c) [H] * W = [] * W

• Jan Hidders