# Re: Distributivity in Tropashko's Lattice Algebra

From: vc <boston103_at_hotmail.com>
Date: 15 Aug 2005 13:48:28 -0700

Marshall Spight wrote:
> vc wrote:
> > Marshall Spight wrote:
> > > A month or so ago we were discussing relational algebras, and
> > > we were looking at a lattice algebra defined in a paper by
> > > Vadim Tropashko. It had two operators, natural join and inner
> > > union.
> > >
> > > One point that was made at the time was that these two operators
> > > are not distributive. (Although they are commutative, associative,
> > > idempotent, and absorbtive.)
> >
> > If you're taking about http://arxiv.org/ftp/cs/papers/0501/0501053.pdf,
>
> Yes.
>
>
> > then I am not sure whether the new algebra (NA) itself is very
> > interesting as applied to the RM. Clearly, the NA implies some RM
> > extension due to the fact that the NA is defined (sort of) over an
> > infinitely countable set of relations and some relations are infinitely
> > countable themselves.
> >
> > The reason for this kind of infinity is the selection and rename
> > definitions both of which rely on joining with infinite relations, the
> > number of potentially required relations being infinite itself.
>
> The reason this doesn't bother me is that I believe the same
> functionality can be had from functions. Functions can model
> some infinite relations quite well. For example, the paper
> mentions the infinite < relation, but the < function would
> work just as well.

Could you please provide an example of an algebraic expression where an infinite relation is replaced with a function? I am too exhausted by the symbol discussion to think of such example myself ;)

Besides, I am not sure the function belongs to the NA (new algebra).

Thanks.

>
> By the way, thank you for responding, since I prefer to talk