Re: Distributivity in Tropashko's Lattice Algebra

From: Marshall Spight <marshall.spight_at_gmail.com>
Date: 17 Aug 2005 19:04:26 -0700
Message-ID: <1124330666.830088.270470@g44g2000cwa.googlegroups.com>

Sorry I'm so far behind on this thread. It'll get worse, too as I'm on vacation starting tomorrow.

Vadim Tropashko wrote:
>
> In D&D algebra
>
> A union DEE != A
> A union DEE != DEE
> A join DEE = A
>
> A union DUM = A
> A join DEE != DEE
> A join DEE != A

This is not my understanding. I was under the impression from TTM that

A <OR> DUM = A
A <OR> DEE = A
also
A <AND> DUM = header(A)
A <AND> DEE = A

(Using <AND> and <OR> to refer specifically to the TTM algebra.)

> > > Now, the novelty is that there is a *third* special element 00 the
> > > relation with with arity = 0 and cardinality = 0, which is not a unit
> > > in Relational Lattice. It is a mapper of a relation into a header
> > > relation!

I thought arity 0, cardinality 0 described DUM. Is that not so? It is possible I'm miscalibrated again.

Marshall Received on Wed Aug 17 2005 - 21:04:26 CDT