Re: Distributivity in Tropashko's Lattice Algebra

From: Marshall Spight <marshall.spight_at_gmail.com>
Date: 15 Aug 2005 12:15:28 -0700
Message-ID: <1124133328.620335.223260_at_f14g2000cwb.googlegroups.com>


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.

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.

Marshal Received on Mon Aug 15 2005 - 21:15:28 CEST

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