Re: In an RDBMS, what does "Data" mean?

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"Paul" <paul_at_test.com> wrote in message news:I91tc.8436$NK4.1009881_at_stones.force9.net...
> x wrote:
> >>The Completeness Theorem proves the "complete" part. i.e. everything
> >>that is true in all models or interpretations of the database will be
> >>provable by the DBMS.
> >
> > Is something that is true in only one model provable by the DBMS ?
> > What this "all models" thing has to do with databases ?
> > Just one model wouldn't be enough ?
>
> No, it'd have to be all models, because the DBMS can only prove things
> that are true under all circumstances, or in the most general case.
>
> Suppose for example I have the following tuples in a relation:
>
> ('Alan', 'Bill')
> ('Bill', 'Chas')
>
> Now in one model, this might mean:
> Alan is an ancestor of Bill.
> Bill is an ancestor of Chas.
>
> So in this model, the tuple ('Alan', 'Chas') could also be legitimately
> added to this relation. i.e the proposition 'Alan is an ancestor of
> Chas' is true.
>
> Similarly if it means "is a brother of'.
>
> But consider the model where it means:
> Alan is a friend of Bill.
> Bill is a friend of Chas.
>
> Then it doesn't follow that Alan is a friend of Chas. It could easily be
> that Alan hates Chas.
>
> So the DBMS shouldn't be able to prove that ('Alan', 'Chas') is a
> legitimate tuple for that relation, because the DBMS has no idea what
> model is being used to interpret the database. And there's no way it
> could have an idea either.

It could have an idea if there is only one model.

> I guess what it is really saying is that the model is larger than the
> theory, in the sense that it has concepts external to the theory. The
> theory can only prove things that are common to all models based on the
> theory (and the Completeness Theorem says it can *always* do this).

Model is about "truth".
Theory is about provability.

> I'm not an expert though, so it's quite possible I've either
> misunderstood the theorem or misapplied it - please correct me if you
> think this is the case.

I'm not an expert either.
But it seems this Completeness and Soundness stuff deals with theorems, not with individual facts.

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