Re: Question about Date & Darwen <OR> operator

paul c wrote:
> Mikito Harakiri wrote:
> > followed by collapse of identical disjunction terms. Likewise, the
> > <AND> operation could be defined. Therefore, the D&D algebra
> > intuitively looks like boolean algebra, but it is certainly not.
> > Absorption, doesn't hold: relation headers monothonically increase, so
> > that there is no way for headers to match. Therefore, this nice boolean
> > logic must break somewhere. Where?
> > ...
>
> i may be missing the question (wouldn't be the first time) regarding 'no
> way for headers to match', but i presume that's why they have <REMOVE>
> in A-algebra (they also require projection in TutorialDee). i'm assuming
> you mean something like a db with a couple of hundred relations each of
> which had, say, ten attributes of which only one is common with some
> other relation, so the equivalent single relation for that database
> would have something like 9 X 200 = 1800 attributes (plus many,many,many
> tuples! likely, no person could compose that expression, but maybe
> there's a reason for a machine to do it. i don't know why, though. if
> that's what you mean by 'break', i guess you're right in theory.

Let A be a relation with attributes x and y. Let B has attributes y and z. Then,

A <OR> (A <AND> B) != A

, since the header of A <AND> B has attributes x,y,z. There is no way the subsequent <OR> operation to reduce it to x,y.

Likewise,

A <AND> (A <OR> B) = A

The fact that D&D have an operation which reduces the header doesn't matter.

> from what i've read, D & D seem to want the traditional 'closure' idea
> of an relational expression, always resulting in a single relation. i've
> wondered why we couldn't have two or more relations in a result. there
> must be times when that's just as pragmatic and cheaper in space terms.
> still, the A-algebra seems a very neat way to get the single closure effect.

Their algebra is closed, no question about it. Received on Sat Sep 03 2005 - 05:05:41 CEST