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

On Sat, 19 Jun 2004 09:27:18 +0100, Paul <paul_at_test.com> wrote:

>> 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.
>
>I think the problem is how do we apply this theorem to relational
>databases. The way I see it, it fits with what I said. :)

For instance it is possible to prove this:

a minus (a minus b) = a intersect b

>When you say "if a relational formula is valid or not" do you mean valid
>as in well-formed or valid as in true?

In true.

> If you mean true, then maybe we
>are just saying the same thing in different ways.

Yes. The antecedent and the consequent are equivalent.

> But I'm seeing the
>result as profound and you're seeing it as trivial.

I am not seeing that as profound or trivial. Godel proved that we can prove all first order language statements, that's all.

>Thus I see Godel's completeness theorem as saying we can therefore prove
>the statement '(forall x) q(x,20)' purely syntactically i.e. without
>considering semantics at all.

Yes, it means that it is a FORMal statement because it is valid depending on the syntactical form and not on the semantics.

> The DBMS only knows syntax, not semantics.
>Thus the DBMS can prove the statement on its own.

Indeed.

>Now it's meaningless to ask whether our new predicate is true or not.

It is always meaningless to ask whether a predicate is true or not :)

What are true or not are the propositions.

>What we want to know is whether any question we ask in semantic terms
>can be answered syntactically. For example the question 'Does Alan like
>rice pudding?'.

var Likes relation { a char, b char };

Likes := relation {
  tuple { a 'Alan', b 'Rice Pudding' }
};

if tuple { a 'Alan' } in (Likes where b = 'Rice Pudding') { a } then   ...

>But I
>think that all first-order questions that can be answered semantically
>will translate to a syntactic question. Which can definitely be answered
>(by Godel's completeness theorem?)

Indeed.

Regards
  Alfredo Received on Sun Jun 20 2004 - 03:37:08 CEST