Re: Question about Date & Darwen <OR> operator

Marshall Spight wrote:
> A <OR> B = { (a,ab,b) |
> ((a,ab) in A cross product Tb)
> union
> ((b,ab) in B cross product Ta)
> }
>
> Is that sufficiently formal? What would constitute a
> sufficiently formal form?

My reply that your expression { (x, y) | x = 1 or y = a } is formal enough is lost somewhere in Google groops:-)

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=%

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 Sat Sep 03 2005 - 03:31:09 CEST