Re: Distributivity in Tropashko's Lattice Algebra
Date: 16 Aug 2005 10:24:01 -0700
Message-ID: <1124213041.085508.224470_at_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
"10" is defined as a neutral element that satisfies the following
01 union A = 0
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 - 19:24:01 CEST