Re: Relational lattice completeness

vc wrote:
>
> I am still not entirely sure what 'completeness' you have in mind.

I gave a full formal definition of what I meant, so, just to be sure, did you understand this definition of completeness that I gave? Or is it that you don't see what it intuitively means?

Roughly, you can summarize it as saying that you have all the algebraic identities that hold, either directly, or indirectly in the sense that that they can be derived from the given list by applying them to each other.

> Simplifying a bit, the relational calculus/algebra are a FOL dialect.
> As such, it is complete in the context of the Godel completeness
> theorem and trivially incomplete in the context of the Godel first
> incompleteness theorem, if treated as a theory with an empty axiom
> set. The 'completeness' terminology is unfortunate but that's life.

Indeed.

> Now, using Codd's classification of what 'complete' means in the
> context of query languages, the RA/RC are 'complete' by Codd's
> definition (as far as I remember) as a standard agains which other
> query languages should be measured (despite the well-known facts about
> inexpressibility of certain questions).

Yes, but that is not the kind of completeness we are talking about here.

> Speaking of the OP question, is he trying to show that his query
> language is as expressive/'complete' as RA/RC, more
> expressive/'complete', or his question is about something completely
> different ?

Since this was originally my question and the OP indicated that he not yet fully understands what I meant, I'm going to answer this for my question: it is about something completely different.

> What's confusing, to me at least, is that in another thread you said
> that the question was about complete theories, that is about
> completeness in the context of the first incompleteness theorem.

It is. Because we talking about a system where we have a semantical notion of truth for algebraic identities and a syntactical one (derivation from the set of given algebraic identies by applying them to each other) and the question is if these two are the same.

• Jan Hidders