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# Re: completeness of the relational lattice

From: Vadim Tropashko <vadimtro_invalid_at_yahoo.com>
Date: Fri, 29 Jun 2007 15:00:30 -0700
Message-ID: <1183154430.194920.265600@e16g2000pri.googlegroups.com>

On Jun 29, 1:40 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 29 jun, 18:20, Vadim Tropashko <vadimtro_inva..._at_yahoo.com> wrote:
>
> > On Jun 28, 3:41 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > > > I invite you to challenge me to show that it can prove an equation
> > > > > that holds. Of course you should also check if all these equations can
> > > > > be derived by you.
>
> > One more challenge:
>
> > <xy> + S + Q = <xy> + S
>
> > where S * [] = [z], and Q header is unconstrained. (I don't see axioms
> > about the lattice bottom element:-)
>
> Sorry. The rules axiomatize the algebra for relations with finite
> headers. When I redid parts of the completeness proof with the
> corrected distribution rule new axioms for W kept on popping up, so I
> decided to do the proof first without W. Once it's completely done I
> might try to put it back in.

I'm OK with no W. Yet the identity in question

<xy> + S + Q = <xy> + S

doesn't involve any of 11,10,1E, so why do we need wide relations in order to prove it? The bottom element 01 is the essence of the problem, not wide relations:

<xy> + 00 = 01

I'm stuck on this identity, because when trying to prove it it seems to me that the only axioms needed are the ones that don't include join operations -- and this is a very limited list. Received on Fri Jun 29 2007 - 17:00:30 CDT

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