Re: In an RDBMS, what does "Data" mean?
Date: Wed, 26 May 2004 10:51:52 +0100
Message-ID: <JMZsc.8405$NK4.1002961_at_stones.force9.net>
Anthony W. Youngman wrote:
>> So I guess the applicability of databases here is that your relations
>> are the axioms of your "theory". Your real-world interpretations of
>> those relations are your "models" of the theory. And the Completeness
>> Theorem assures you that everything you expect to be true in the real
>> world will in fact be provable by the DBMS.
>
> And if they turn out to be false in the real world and provable in the
> DBMS, then the DBMS theory is wrong ... (or the DBMS predicts something
> is false when it turns out to be true ...)
Well, the Completeness Theorem has a converse called the Soundness Theorem (http://en.wikipedia.org/wiki/Soundness_theorem), which assures us that first order logic is consistent. i.e. everything that you can prove in the DBMS is true in real life. This was known long before the Completeness Theorem I think, and is easier to prove.
> Or if you can't prove it in the DBMS, then the theory is incomplete ...
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.
Note that Godel's Incompleteness Theorem is something slightly different. That's really talking about the completeness of theories that just happen to be manipulated with first order logic. The Completeness Theorem is talking about the completeness of first-order logic itself. So in the first instance you could say first order logic is being a meta-language, but in the second instance it is just being a language.
Paul. Received on Wed May 26 2004 - 11:51:52 CEST