Re: More on lists and sets

Mikito Harakiri wrote:
> Jan Hidders wrote:
> > Mikito Harakiri wrote:
> > > Less chatty version:
> > > http://arxiv.org/ftp/cs/papers/0603/0603044.pdf
> >
> > Mikito, do you know if Vadim's axiomatization is complete? I mean, are
> > two queries equivalent iff the algebraic identities allow me to rewrite
> > one to the other? Or might there still be algebraic identities missing?
>
> Axiomatization of relational algebra -- that was the question you asked
> on c.d.t back in 2001?

Yes, but now I'm asking a slightly different question because we're dealing with a different algebra.

> Relational lattice theory is not complete. Many parts still remain
> informal -- Spight distributivity criteria among them. It could be
> written formally, but this expression
>
> (A /\ C /\ 00) \/ (B /\ C /\ 00) \/ (A /\ B /\ 00)
> = (B /\ 00) \/ (C /\ 00)
> ==>
> A /\ (B \/ C) == (A /\ B) \/ (A /\ C)
>
> doesn't look like a satisfying axiom.

Understood, but let's start first with a simpeler question. Is the axiomatization complete if we only consider /\ and \/? (So no 00, 01, 10 and 11.)

• Jan Hidders