Re: Question about Date & Darwen <OR> operator

"Mikito Harakiri" <mikharakiri_nospaum_at_yahoo.com> wrote in message news:1125711068.995070.322110_at_g44g2000cwa.googlegroups.com... [...]
> Well, the formal definition of <OR> and <AND> seems to be very
> consistent with boolean logic. Take
>
> Relation A
> x y
> - -
> 1 a
> 2 b
>
> and
>
> Relation B
> y z
> - -
> a #
> b %
>
> Then, formally relation A is a proposition
>
> x=1 & y=a \/ x=2 & y=b
>
> while relation B is
>
> y=a & z=# \/ y=b & z=%
>
> The <OR> is just formal disjunction
>
> x=1 & y=a \/ x=2 & y=b \/ y=a & z=# \/ y=b & z=%
>
> that could be equivalently transformed into
>
> x=1 & y=a & z=# \/
> x=1 & y=a & z=% \/
> x=2 & y=b & z=# \/
> x=2 & y=b & z=% \/
> x=1 & y=a & z=# \/
> x=2 & y=a & z=# \/
> x=1 & y=b & z=% \/
> x=2 & y=b & z=%
>

The above transformation ain't correct. In fact such transformation cannot be performed because x,y and z's domains are not specified.

> 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?
>
Received on Mon Sep 05 2005 - 19:12:53 CDT