Re: Comments on Norbert's topological extension of relational algebra

On Tuesday, December 15, 2015 at 8:14:17 AM UTC-8, Jan Hidders wrote:
> What *I* am interested in is the connection with this work:
>
> http://alpha.uhasselt.be/~lucp1080/queries_reals.pdf

Do you prefer to work with algebraic or semi-algebraic constraints?

Here is how Heath's theorem from database dependency theory is made obvious in algebraic settings. Basically we have: 1. A system of constraints in 3 variables x,y,z 2. A function x->y
We need to reorganize the system's constraints into two parts: the ones expressed in variables x and y only, on one hand, and the other in x and z. For the first system we take the equation that defines the active domain x together with the equation that explicitly defines FD x->y. For the second system, we take the whole original system, and eliminate y by substitution its formula in terms of x. https://vadimtropashko.wordpress.com/2014/01/03/analytic-view-of-functional-dependency/

I struggle to prove Heath's theorem for semialgebraic sets. For example, is it possible to have functional dependency which is a function but not expressible polynomially? Received on Sun Dec 20 2015 - 10:27:15 CET