Re: completeness of the relational lattice

On Jun 22, 10:36 am, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
> - R : a relation name
> - Expr /\ Expr : the natural join
> - Expr \/ Expr : the inner union
> - 00 : the empty relation with empty header
> - 01 : the relation with the empty tuple and empty header
> - 10 : the empty relation with the set of all attributes as header
> - 11 : the relation with all tuples over all attributes
> - E : the "universal" equlity relation

Axioms:
01 /\ R = R
10 \/ R = R

R = (R /\ 00) \/ (R /\ 11)
00 /\ (R \/ S) = (00 /\ R) \/ (00 /\ S)
11 \/ (R /\ S) = (11 \/ R) /\ (11 \/ S)

I don't seem to be able to express the properties of equality E in pure equational settings. The have to be some premises... Received on Fri Jun 22 2007 - 19:56:21 CEST