Re: What to call this operator?

Jon Heggland wrote:
> In article <1120156799.149832.136240_at_o13g2000cwo.googlegroups.com>,
> mikharakiri_nospaum_at_yahoo.com says...
> > > x y <= A
> > >
> > > That's right, instead of bracket notation A(x,y) saying that relation A
> > > has attributes x and y, we can just write "A >= x y" implying that A is
> > > a superset of join of empty relations x and y.
> >
> > On a symmetrical note, lets use capital letters X, Y etc to denote an
> > infinite relation each of which is a full domain. Then
> >
> > A <= X Y
>
> Nice, but is it not also so that A >= x y z and A <= X Y Z for A(x,y)?
> Which makes that notation less useful....

A >= x y z transitively follows from

A >= x y x >= x y

However A <= X Y Z doesn't hold. Ascii diagram for the lattice A(x,y) = {(1,a)} with domains X = {1,2} and Y = {a,b} illustrates this assymetry

.....xy
.../.|.\
../..|..\
.x...A...y
.|../|\..|
.|./.|.\.|
.|/..|..\|

.|../.\..|
.|./...\.|
.|/.....\|
.X.......Y
..\...../
...\.../
....\./
....{}