Re: Dee Dum

vc wrote:
> Vadim Tropashko wrote:
> > 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).

Well, the point is that Relational Lattice is certainly something more than just a lattice. What if we define Relational Lattice as a [normal] lattice with a special element 00 that satisfies an additional Spight distributivity axiom

[(A join C) union (B join C) union (A join B)] join 00 == [B union C] join 00
==>
A union (B join C) == (A union B) join (A union C)

Of course, this formulation is immature yet. Received on Wed Aug 17 2005 - 13:54:29 CDT