Re: Distributivity in Tropashko's Lattice Algebra

vc wrote:
> Vadim Tropashko wrote:
> >
> > "01" is defined as a neutral element that satisfies the following
> > identities:
> >
> > 01 join A = A
> > 01 union A = 0
>
> Let 'join' be the natural join from your aticle, 'union' the
> generalized union from your article, '01' the relation with arity 0 and
> card 1, '10' the relation with the header of probably countably
> infinite cardinality (since it's a union of all the headers in some
> implementation of your algebra), '00' the relation with arity zero and
> cardinality zero.
>
> Then '01' join A = A
> but
> '01' union A = '00' (unless '0' was typo)

I see that you've already addressed this point. I'll add that A is bounded between the tattice least and greatest element

01 < A < 10

while

A and 00 is not comparable

> >
> > "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.
>
> It's unclear what you mean. See below.

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




> > 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!

It's a novelty for me;-) Received on Tue Aug 16 2005 - 22:32:25 CEST