Re: Relational lattice

Vadim Tropashko wrote:
>
> Is it possible to express transitive closure in a finite set of
> equations as well?

Good question. Very good question. I suspect not, but I'm not sure and certainly have no proof. I do know that you can if you use the nested relational algebra.

By the way, I just ran into a somewhat related paper. It's probably not exactly what you are looking for, but you might be interested in it:

"Solving equations in the relational algebra"

http://arxiv.org/abs/cs.LO/0106034

> BTW, I just came across
> http://c2.com/cgi/wiki?RelationalAlgebra
> describing the "simplified algebra in the Third Manifesto". (I confess
> that I don't have a copy of any manifesto book:-).

I won't tell. :-)

> The AND operator is
> a natural join, but the OR is defined differently! It is immediate,
> that the Third Manifesto definition doesn't respect the absorption law:
> A OR (A AND B) header should be the union of the A and B headers,
> therefore the result can't be A. Without absorption law the structure
> is merely a semilattice, where the order induced by the meet operation
> -- OR -- is different from the order induced by the join. The nice
> feature of the manifesto algebra is that it respects distributive law.

So, how about the cylindric set algebras? For a short description look for "Applications of Alfred Tarski's Ideas in Database Theory".

• Jan Hidders