Re: Functional dependency is multivalued dependency

Jan Hidders wrote:
> Do you already know how to represent the FD in RL equations?

I(x, y_1, z_1) /\ I(x, y_2, z_2) /\ `y_1!=y_2` = `x y_1 y_2 z_1 z_2`

Informally, we transform the "not exist" condition into an equation that evaluates some expression to be an empty relation. We take two relations with the same attriubute x and two different y's, join them and it has to be an empty relation.

When a relation symbol has attribute variables listed in parenthesis it is not a genuine algebraic identily. This can be handled via renaming.

Let's assume that I has attributes x, y and z, which we don't have to list in brackets anymore. Then

I(x, y_1, z_1) = (I /\ `y=y_1` /\ `z=z_1`) \/ 'x y_1 z_1' I(x, y_2, z_2) = (I /\ `y=y_2` /\ `z=z_2`) \/ 'x y_2 z_2'

Therefore we can rewrite functional dependency constraint equation in terms of the relation symbol I with standard list of attributes x,y,z.

Clearly any firhter progress has to leverage the laws around the two special relations that appear everywhere: equality and inequality relations. But what are the RA axioms that equality and inequality satisfy to? To begin with, I have trouble writing idempotency, symmetry and transitivity for equality in RA terms... Received on Sun Apr 30 2006 - 20:52:44 CEST