Re: Notions of Type

paul c wrote:
> Marshall wrote:
> > ...
> > The Tropashko algebra's operators ARE commutative,
> > and associative, and absorbitive and idempotent
> > to boot! And semi-distributive as it turns out. And
> > there's only two of them. Now THAT is an algebra
> > for you!
>
> I don't mean to criticize TA's motivation for the simple reason that I'm
> not competent to talk about lattice algebra properties.
>
> But a perhaps trivial comment is that D&D claim their algebra can also
> be reduced to two operators as well, take your choice, NAND and REMOVE
> or NOR and REMOVE.

Yeah, sorta by analogy with boolean algebra. That was actually a pretty interesting result they got. I didn't feel like it was an endpoint result, though, for a few reasons. It still has the only-sorta-algebraic REMOVE in it. It brings up negation, which can be problematic. They also didn't analyze the algebraic properties as fully as was necessary; I believe I recall Vadim pointing out that their algebra lacks absorbtion, an important property.

> For some reason I want to compare TA to D&D algebra, maybe this is
> wrong-headed but I do see a similarity in the two approaches,

Sure.

> what D&D
> call 'treating operators as relations', for example TA seems to apply
> this idea to projection, whereas D&D use it to get rid of operators like
> EXTEND and SUMMARIZE, if I recall right.

Marshall Received on Sat Aug 19 2006 - 20:31:46 CEST