Re: Onto a potential relational manipulation language

On Dec 12, 12:49 pm, vadim..._at_gmail.com wrote:
> On Dec 12, 11:58 am, paul c <toledobythe..._at_oohay.ac> wrote:

> > ... such as the "multi-relations" Darwen

> Missing information...yawn.

I take my yawn back. Consider a multi-relation with only one attribute that has missing information. It is convenient to represent it as the outer union of genuine relations x and y: x + y. (For most readers who familar with TTM and "A"lgebra I remind you that outer union is D&D <AND> operator). How does multi-relation interacts with (natural join)? Easy, distributivity

(x + y) ^ z = (x ^ z) + (y ^ z)

is a theorem in RL. Next how to do projection over multi-relation? Let project x + y onto a subset of "normal" attributes, those that don't have missing information. Formally, we represent those attribute as an empty relation z, that is

z ^ R00 = z

Next,

(x v y) v z = z

that is z contains a subset of attributes common to x and y. With these assumptions the projection

(x + y) v z

is the same as

(x v y) v z

Again, this is automatic deduction in prover9. By being able to change outer union to inner union we proved that the result of of projecting multi-relation to a subset of "normal" attributes is genuine relation (without any missing info). Received on Fri Dec 12 2008 - 22:29:06 CET