Re: Relational symmetric difference is well defined

On May 31, 6:40 pm, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote innews:1180628927.976321.267880@a26g2000pre.googlegroups.com:
>
> > On May 30, 8:52 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
> >> Can you clarify the difference between set containment join and set
> >> equality join? The inverse of join is much on my mind these days.
>
> > Set equality join
>
> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}={y|A(y,z)} }
>
> > Set containment join
>
> > A(x,y)/=B(y,z) is {(x,z)| {y|A(x,y)}>{y|A(y,z)} }
>
> > where the ">" is "subset of".
>
> The above formulas obviously are no longer first-order expressions.
> Along with the increased expressive power (e.g. it's trivial to define a
> powerset), you will reap the usual drawbacks of the higher order logic.

Can you expand on that?

Although it's clear the above operator(s) are different in kind from join and union, it's not obvious (to me anyway) that this difference translates into higher-orderness.

Marshall Received on Fri Jun 01 2007 - 03:57:35 CEST