Re: header part of the value?

On 28 feb, 22:27, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
> On Feb 28, 1:16 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
>
>
> > On 28 feb, 21:58, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
>
> > > On Feb 28, 11:35 am, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:
>
> > > > Let me reiterate the generalized relation idea one more time, on a
> > > > level perhaps more digestable for wider audience. Consider classic
> > > > relation
>
> > > > "The person first name is ..."
>
> > > > Normally, we don't write the whole sentence in the relation header (we
> > > > focus exclusively on named perspective, of course) and abbreviate it
> > > > to just
>
> > > > Name
> > > > -----
> > > > Scott
> > > > Mike
>
> > > > The concept of domain has been introduced to resolve questions weather
> > > > this relation is allowed to be joined with something like
>
> > > > "The ship name is ..."
>
> > > > All we do when allowing generalized relations is admitting predicates
> > > > like this:
>
> > > > "The variable x is greater or equal than ..."
>
> > > > and insisting that the whole sentence matters as a relation header.
>
> > > Here is little more background. The inspirational paper is Grumbach&Su
> > > "Finitely Representable Databases". They introduced the concept of
> > > finite representativity, for example the relation {x:x>=0} is not
> > > finitely representable as a classic relation on infinite domain, but
> > > is finitely representable in more general sense. However, after few
> > > pages they lost me: I can't understand where are they heading with
> > > this idea, why compactness theorem, Ehrenfeuht-Frausse gaimse and
> > > PTIME matter. From practical perspective, one would think the first
> > > thing they should discuss is an algebra to conveniently operate these
> > > finite representations.
>
> > The complexity and computability results indicate to which extent such
> > an algebra is possible and/or useful. Besides, why do you think such
> > an algebra is necessary? What is necessary is that you can ask queries
> > and that there are algorithms to compute them. An algebra is just one
> > possible solution for that.
>
> > > Anyway, returning to the example
>
> > > Q:
> > > x + 3 = y \/
> > > x + 5 = y
>
> > > Is it binary or unary relation? Sure it is a binary relation Q(x,y) in
> > > classic sense, but it is not finitely representable!
>
> > Why do you think it is not finitely representable?
>
> Sure, there is infinite number of tuples in
>
> Q(x,y) = {(x,y) | exists t in N such that x = t and (y = t + 3 or y =
> t + 5)}

That does not mean it is not finitely representable. Or are you using a different definition than Grumbach and Su?

• Jan Hidders