# Re: Relational lattice

Date: Thu, 10 Mar 2005 21:13:15 GMT

Message-ID: <LL2Yd.34677$f73.3168353_at_phobos.telenet-ops.be>

Vadim Tropashko wrote:

*>
*

> Is it possible to express transitive closure in a finite set of

*> equations as well?
*

"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