Re: Relational lattice completeness

vc wrote:
> Jan Hidders wrote:
> > vc wrote:
> > >
> > > 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.
>
> They would be the same for a complete (in the sense of the first
> incompletenes theorem) system so finding out whether this is the case
> would amount to showing if the system in question is complete or not.

Not necessarily because the syntactical notion of truth is not the usual one. It's related but not the same.

> However, I am not sure why that may be practically important.
> Arithmetic incompleteness does not prevent anyone from balancing one's
> checkbook.

Having a full and simple axiomatization makes it possible to write query optimizers that do a more thorough search of the "optimization space", and if you know you are complete then you are sure that you need not look further for any other rules.

• Jan Hidders