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

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"x" <x-false_at_yahoo.com> wrote in message news:40b4b70b$1_at_post.usenet.com...
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> "x" <x-false_at_yahoo.com> wrote in message
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> > "Paul" <paul_at_test.com> wrote in message
> > news:I91tc.8436$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.
>
> For example one could build a model in such a way that:
> Friend(Alan,Bill) means ancestor(bill,alan)
> Ancestor(Alan,Bill) means friend(bill,alan)

Or Alan and Bill could mean the same person Dan.

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