Re: Relational lattice completeness

Jan Hidders wrote:
> vc wrote:
> >
> > I am still not entirely sure what 'completeness' you have in mind.
>
> I gave a full formal definition of what I meant, so, just to be sure,
> did you understand this definition of completeness that I gave? Or is
> it that you don't see what it intuitively means?

No, I was not sure what kind of completeness we were talking about since the word is abused so much. Intuitive meaning would be helpful for sure.

>
> Roughly, you can summarize it as saying that you have all the algebraic
> identities that hold, either directly, or indirectly in the sense that
> that they can be derived from the given list by applying them to each
> other.

OK.

[...]
> the RA/RC are 'complete' by Codd's
> > definition (as far as I remember) as a standard agains which other
> > query languages should be measured (despite the well-known facts about
> > inexpressibility of certain questions).
>
> Yes, but that is not the kind of completeness we are talking about
> here.

OK.

>
> > Speaking of the OP question, is he trying to show that his query
> > language is as expressive/'complete' as RA/RC, more
> > expressive/'complete', or his question is about something completely
> > different ?
>
> Since this was originally my question

I apologize for the misattribution.

> and the OP indicated that he not
> yet fully understands what I meant, I'm going to answer this for my
> question: it is about something completely different.
>
> > What's confusing, to me at least, is that in another thread you said
> > that the question was about complete theories, that is about
> > completeness in the context of the first incompleteness theorem.
>
> It is. Because we talking about a system where we have a semantical
> notion of truth for algebraic identities and a syntactical one
> (derivation from the set of given algebraic identies by applying them
> to each other) and the question is if these two are the same.

They would be the same for a complete (in the sense of the first incompletenes theorem) system so finding out whether this is the case would amount to showing if the system in question is complete or not. However, I am not sure why that may be practically important. Arithmetic incompleteness does not prevent anyone from balancing one's checkbook.

>
> -- Jan Hidders
Received on Fri Apr 07 2006 - 19:10:36 CEST