Re: Relational lattice completeness

Jan Hidders wrote:
> It is. Because we talking about a system where we have a semantical
> notion of truth for algebraic identities and a syntactical one
> (derivation from the set of given algebraic identies by applying them
> to each other) and the question is if these two are the same.

What makes your question hard is that the idea of formal derivation of algebraic identities is not mature enough yet.

Consider the chain of rewritings for push-select-through-project on page 7. On step 8 the Spight criteria is applied. It's highly informal. We looked on the set of attributes of the each relation, check that they meet the condition, then apply the distributivity law. This step is highly informal. It has to be be broken down to a series of smaller steps which are simple applications of aximoatic equalities.

Next, consider the step #13 in push-cross-through-project rewritings on page 8. Informally, it is obvious that

`x` /\ B(z) = `xz`

(cross product of the empty relation `x` with the other relation is empty)
but what axiom identity were appied on this step exactly? Received on Fri Apr 07 2006 - 18:25:19 CEST