# Re: Distributivity in Tropashko's Lattice Algebra

Date: 15 Aug 2005 13:48:28 -0700

Message-ID: <1124138908.628722.243250_at_g47g2000cwa.googlegroups.com>

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

*> about this than to talk about what the name for the symbol of
**> the string that represents 1234 is called.
**>
*

rather boring, aint it ;)

*>
**> Marshal
*

Received on Mon Aug 15 2005 - 22:48:28 CEST