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

Date: Wed, 2 Jun 2004 13:28:07 +0300

Message-ID: <40bdaad0_at_post.usenet.com>

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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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