Re: Dee Dum

Vadim Tropashko wrote:

> Let's be a little bit pedantic, and refer to DEE and DUM as elements of
> D&D algebra, while defining 10 as a join of all the elements (the
> greatest element) and 01 as a union of all the elements (the least
> element). Then,
>
> 01 < A < 10
>
> for any A. Hence, the two inequalities rewritten as 4 identities
>
> 01 join A = A
> 01 union A = 0

Actually, if you define '01' to be the [generalized] union, then

01 union A = 01

>
> 10 join A = 10 (corrected:-)

Please ignore my previous question.

> 10 union A = A
>
> It was precisely this set of identities that I losely compared with DEE
> and DUM identities in the D&D algebra. Although, this comment is just a
> reiteration of the lack of symmetry in D&D algebra that has been
> already discussed. (The incompatibility of the order relations imposed
> by the upper and lower semilattice).
>

Yes, but the symmetry comes at the heavy price of having infinite reltions.

> Now, the 00 element is a whole different story. It is not comparable to
> any element in the lattice except the header and rowid relations.
> Hmm... How to define it formally?

It probably cannot be the result of any operation in your algebra unless one of the operands is '00' (I did not look too closely at the 'difference' implementation). In D&D it's trivial: '00' = Project({}, A-A), where {} is an empty set and A-A is an empty relation with an arbitrary header (a difference over the same relation). Received on Wed Aug 17 2005 - 20:31:39 CEST