Re: Relational Lattice, what is it good for?

Mikito Harakiri wrote:
> ...has a chance to be
> repaired.

Indeed. Withoul loss of generality, we could focus on relations with headers

A(x,u,w,t)
B(y,u,v,t)
C(z,v,w,t)

They don't satisfy Spight criteria, however. The relations that satisfy are

A(x,t)
B(y,v,t)
C(z,v,t)

Working out the left side of distributivity equation we have:

A && (B || C) = { (x,v,t) | A(x,t) and ( exists y B(y,v,t) or exists z C(z,v,t) ) }

while the right side is

(A && B) || (A && C) =
{ (x,v,t) | (exists y A(x,t) and B(y,v,t)) or (exists z A(x,t) and C(z,v,t)) }

They are equivalent since existential quantifier can be moved into the outer most scope.

On the other hand, if we consider the relations, that don't satisfy spight criteria, say

A(x,u,t)
B(y,u,v,t)
C(z,v,t)

Then we'll have the the u variable stuck under existential quantifier in the left side expression and free on the right side. Received on Sat Feb 18 2006 - 02:46:31 CET