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

Todd B wrote:
> In a way, however, Godel's theorem is pertinent because it touches on
> the fact that a database, no matter what its design is or underlaying
> structure is, will 'definitely' not be able to answer every question
> we want to ask it.

Are you certain this is true?

As I understand it:
1) Godel's Incompleteness theorem only applies to system that are powerful enough to model arithmetic.
2) It's impossible to model arithmetic using only first-order logic. 3) Relational theory (which basically *is* first-order logic) is actually both complete and consistent.

I'm not a professional logician though, and I know Godel's results are very open to misinterpretation, so I could well be wrong. I guess it depends on the exact definitions of "model", "theory", "system", "logic" etc., and what exactly we mean by "complete" and "consistent".

Also, does it actually matter? Because for example suppose I'm right and relational theory is complete, there are still questions like the transitive closure which can't be answered. That's because these questions can't even be written down in first order logic so they are meaningless within the system (so the system is still complete). But they are meaningful in a "real-world" sense, because we are thinking in a larger system which includes second-order logic.

I suppose at least we would know that in theory, every query that it is possible to formulate in some given relational query language can be answered.

Paul. Received on Fri May 21 2004 - 21:08:55 CEST