Oracle FAQ Your Portal to the Oracle Knowledge Grid
HOME | ASK QUESTION | ADD INFO | SEARCH | E-MAIL US
 

Home -> Community -> Usenet -> comp.databases.theory -> Re: completeness of the relational lattice

Re: completeness of the relational lattice

From: Jan Hidders <hidders_at_gmail.com>
Date: Fri, 22 Jun 2007 18:20:50 -0000
Message-ID: <1182536450.083309.219960@o61g2000hsh.googlegroups.com>


On 22 jun, 19:36, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
> On Jun 22, 3:08 am, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > > We cannot distribute in general, but we have a specific distribution rule:
>
> > > > (1) r /\ ((s \/ [H]) \/ (t\/[H])) = r /\ (s \/ [H]) \/ r*(t \/ [H])
>
> > > Which is BTW a very limited case embraced by Spight criteria.
>
> > Indeed. But it is a simple equation, no premises.
>
> Your premise is that H is a set of attributes which is a subset of
> attributes of relations s and t

No, any set of attributes H will do.

> > > BTW, why don't we define square brackets [R] as an unary operator,
> > > expressed in my notation as
>
> > > [R] = R /\ 00
>
> > What is R? In [R] it is a set of attributes. So a set of attributes is
> > a valid expression in your syntax? I'm not sure what that means.

Sorry, I missed your point there. The problem with [R] is that is doesn't allow me to define a projection for an arbitrary set of attributes.

> > Could
> > you give a complete definition of your syntax just like I did?
>
> - 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

And extended with [R] I assume. Can you prove that you can express all queries in UCQ?

> Once again, I'm not convinced about syntax until I see a convincing
> set of axioms.

We have to start somewhere. Otherwise I'm afraid we are not going to get anywhere. Even an ugly axiomatization is better then no axiomatization at all.

Received on Fri Jun 22 2007 - 13:20:50 CDT

Original text of this message

HOME | ASK QUESTION | ADD INFO | SEARCH | E-MAIL US