Re: Notions of Type

paul c wrote:
> Marshall wrote:
> > [...]
>
> Thanks, and
>
> Okay, maybe you are right but what if project is not binary but unary?
> Isn't the idea of treating it as a binary operator arbitrary? Is it
> enough to say that a projection joined with the relation it was produced
> from results in that same relation? Just wondering ...

I don't see anything wrong with unary operators. But we can't really do PROJECT as a unary operator, because we don't have enough info to know what operators should be left when we're done. (If we were dealing with binary relations, we could define FIRST and SECOND, but that's of little use to us here.)

> As I mentioned before, the only problem I had with the TA is that it
> seemed that certain logical behaviour was missing, eg. de Morgan's laws.
> I imagined this might create some difficulty for the CWA.

Sure. The thing is that DeMorgan's applies to Boolean algebras, and the Tropashko algebra is a lattice algebra, not a boolean algebra. (In fact it's two lattice algebras in one.) There's no NOT operator in the Tropashko algebra.

Marshall Received on Fri Aug 18 2006 - 08:06:21 CEST