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

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"Paul" <paul_at_test.com> wrote in message news:AK8vc.9364$wI4.1212916_at_wards.force9.net...
> x wrote:
> > Prolog is based on first order logic. What is the difference between
> > the Prolog way and the Relational Model way of representing data ?
>
> Hmm according to one website: "The difference between Prolog and a
> Relational DBMS is that in Prolog the relations are stored in main
> memory along with the program whereas in a Relational DBMS the relations
> are stored in files and the program extracts the information from the
> files." So from this it would seem that logically they are the same.

There are other differences.
For example there are no candidate or foreign keys in Prolog.

> >> Or upwards to higher-order logic, although I don't know if
> >> incompleteness becomes an issue then. Maybe because we are always
> >> dealing with unbounded but finite systems it doesn't apply or
> >> something. I think if you go this route you end up with things like
> >> Datalog or Prolog.
> >
> > Prolog is not higher-order logic.
>
> OK, I'm not that familiar with Prolog.

If you are interested, you can start at: http://www.lim.univ-mrs.fr/~colmer/
http://www-lp.doc.ic.ac.uk/UserPages/staff/rak/rak.html

> But I see a few references to second-order logic in Prolog:

The name Prolog came from the French of "Programming in Logic" There are many variants of "Prolog" today.

http://cs.wwc.edu/~aabyan/LABS/LogicProgramming/2ndorder.html http://www.scms.rgu.ac.uk/staff/smc/teaching/kbp3/kbp3/node7.html

> > And first order logic is "incomplete" also because of the
> > "in all models" stuff.
>
> I don't really understand what your problem is with this.
>
> Here's another statement of Godel's Completeness Theorem:
> "If T is a set of axioms in a first-order language, and a statement p
> holds for any structure M satisfying T, then p can be formally deduced
> from T in some appropriately defined fashion."
>
> They're using the word "structure" for "model" but the same concept. Now
> surely this is just what you'd intuitively expect?
>
> For example consider our theory T is group theory. One structure that
> satisfies the group theory axioms is that of abelian (commutative)
> groups. In this structure every element commutes with every other
> element. But this is not the case for the general theory of groups. For
> something to be a universal property of groups, it must be true for
> *every* possible structure that satisfies the group axioms. And the
> theorem says that then you can *always* prove the property in the theory
> T alone (i.e. without reference to any of the structures based on the
> theory T).

But I'm interested in properties of a particular structure S, not in the properties of some theory T that happen to describe some aspects of S.

> I'm acutally wondering as well whether all this talk of Godel is
> irrelevant anyway because in databases we are only dealing with finite
> sets of axioms. Possibly second order logic is complete when you have a
> finite number of axioms? I'll have to do a bit more Googling.

In databases we deal with facts, not with finite sets of axioms. Metamathematics deal with sets of axioms and theorems.

Have you seen :
http://www-csli.stanford.edu/hp/CVandNR.pdf http://www-csli.stanford.edu/hp/Reflections.pdf

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