Re: completeness of the relational lattice

On 23 jun, 01:05, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
> On Jun 22, 3:31 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > I can probably simplify using Marshall's rule. Assuming I
> > have a function A(e) that gives the header of the result of e:
>
> > r /\ (s \/ t) = (r /\ s) \/ (r /\ t) if (A(r) * (A(s)) - A(t) is
> > empty and (A(r) * A(t)) - A(s) is empty
>
> OK, to summarize we have 2-sorted algebra:
> 1. Relations (which is lattice)
> 2. Relation headers (which is standard BA)
> The function A maps relations to headers, and enjoys the following
> rule
> A(R \/ B) = A(R) intersect A(B)
> Note that function A is not a homomorhism, that is the dual identity
> A(R /\ B) = A(R) union A(B)
> doesn't hold.

Really? It doesn't? Can you give a counterexample?

> Please also note, that in my notation the algebra is not many sorted.

Duly noted.

> BTW, if you have finction A, then we probably don't need element 00,
> right? (The element A(01) is just an empty set in the boolean algebra
> of headers, not the lattice element 00)

Not sure what you are asking. A is not really part of the algebra, but only used in describing the rules, so A(01) is not an expression in the algebra.

• Jan Hidders