Re: Dee Dum

Vadim Tropashko wrote:
> 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.

Why is this specific relation bothering you so much ? You can consider it as the FALSE select predicate (when you express select through a natural join). You have plenty of those with some being infinite (x <y). Received on Wed Aug 17 2005 - 22:03:47 CEST