Re: Distributivity in Tropashko's Lattice Algebra
Date: 15 Aug 2005 11:18:24 -0700
Message-ID: <1124129904.211195.198980_at_g43g2000cwa.googlegroups.com>
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,
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.