Re: Distributivity in Tropashko's Lattice Algebra

From: Vadim Tropashko <vadimtro_invalid_at_yahoo.com>
Date: 16 Aug 2005 10:24:01 -0700
Message-ID: <1124213041.085508.224470@g44g2000cwa.googlegroups.com>

> Note however,
> that in the article there is a certain controversy about TABLE_DUM and
> TABLE_DEE. Apparently, in the attempt to make them symmetrical
>
> TABLE_DUM is defined with arity = 0, cardinality = *1*, and
> TABLE_DEE is defined with arity = 1, cardinality = 0

There is no controversy. The article introduced the two lattice units that I can't reproduce pictirially here due to ascii constraint. I have to introduce ascii-frendly symbols:

"01" is defined as a neutral element that satisfies the following identities:

01 join A = A
01 union A = 0

"10" is defined as a neutral element that satisfies the following identities:

10 join A = A
10 union A = A

Note that DEE and DUM in D&D algebra satisfy only a single identity each.

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!

00 join A = a Received on Tue Aug 16 2005 - 12:24:01 CDT