Re: header part of the value?

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)} Received on Thu Feb 28 2008 - 22:27:47 CET