Re: Relational Lattice, what is it good for?

Mikito Harakiri wrote:
> Marshall Spight wrote:
> > > Alternatively, you have to use existential qualifier, as Jon written in
> > > the old exchange.
> >
> > I only vaguely recall this exchange, and I seem to remember that
> > I didn't understand it at the time.
>
> A(x,y) || B(y,z) = { y | exists x A(x,y) or exists z B(y,z) }

Ah, I see.

> > > This step [4-5] is not obvious. Again, careful manipulation would involve
> > > projection.
> >
> > I don't understand the problem. This step relies only on the
> > distributivity of the boolean algebra; note that the operands of the
> > boolean operators ("and", "or") in the expressions are syntactically
> > unchanged between steps 4 and 5. I assumed I could rely on
> > boolean distributivity; was that an unjustified assumption?
>
> Oops, I'm sorry I meant 3->4.

One goes from 3 to 4 by applying the definition of the inner union. The two operands are both projected over the intersection of their attributes. Because there are seven categories of attributes, (depending on which relation(s) they are in) the notation is laborious. But it is the simplest one I could think of.

Marshall Received on Sat Feb 18 2006 - 18:21:39 CET