Re: how many RDF* triples?

I was wondering about the difference with
_:a :p (_:a :p (_:a :p (_:a :p ...)))
which is an RDF triple with an infinite number of elements

-- https://josd.github.io/ <http://josd.github.io/>


On Thu, Oct 15, 2020 at 11:32 AM Pierre-Antoine Champin <
pierre-antoine.champin@ercim.eu> wrote:

> Argh, I realize that I hit "reply" instead of "reply all", when
> answering Peter's original message :-/
>
> To sum up our exchange:
>
> * the "infinitely nested" triples suggested by Peter should not, in my
> opinion, be allowed, and I don't think Olaf's intention was to allow them;
>
> * hence, I reverted the definition of RDF* triples to Olaf's original
> definition (from the paper), which makes this restriction more explicit;
>
> * with this restriction, I believe that the set of RDF* triples is
> "only" countably infinite, as any RDF* triple can be serialized into a
> (finite) string.
>
> On 15/10/2020 09:06, Olaf Hartig wrote:
> > Hi Pat,
> >
> > I understand the difference between uncountably infinite sets and
> countably
> > infinite sets, and I see that the set of all possible RDF* triples is
> > uncountably infinite. So, in that sense, yes, my comparison to literals
> was
> > imperfect as it was only about infinity without distinguishing between
> the
> > countable and uncountable variant.
> >
> > The main question is whether the uncountable infinity of all RDF*
> triples may
> > cause problems. I don't see how it may cause problems.
> >
> > Thanks,
> > Olaf
> >
> >
> > On onsdag 14 oktober 2020 kl. 16:27:03 CEST Patrick J Hayes wrote:
> >> Hi Olaf
> >>
> >> Not quite the same issue with literals. There are countably many
> literals,
> >> just as there are countably many possible IRIs and countably many RDF
> >> graphs. But if Peter is correct, there are uncountably many RDF*
> triples.
> >> An uncountable infinity is a lot more than a countable infinity.
> >>
> >> Pat
> >>
> >>> On Oct 14, 2020, at 8:00 AM, Olaf Hartig <olaf.hartig@liu.se> wrote:
> >>>
> >>> Hi Peter,
> >>>
> >>> Right, there is no bound on the nesting depth. However, I don't think
> that
> >>> this may cause problems.
> >>>
> >>> By the way, the set of literals is infinite as well, so you have the
> same
> >>> issue with RDF triples.
> >>>
> >>> Olaf
> >>>
> >>> On onsdag 14 oktober 2020 kl. 08:46:52 CEST Peter F. Patel-Schneider
> > wrote:
> >>>> I was looking at https://w3c.github.io/rdf-star/ and got to
> wondering how
> >>>> many RDF* triples are there?  It appears to me that there are an
> >>>> uncountable number of RDF* triples because there is no axiom of
> >>>> foundation
> >>>> for RDF* triples.
> >>>>
> >>>> So the following is an RDF* triple:
> >>>>
> >>>> _:a :p << _:a :p << _:a :p << _:a :p ... >> >> >>
> >>>>
> >>>> So an RDF* triple could have an infinite number of elements and so
> there
> >>>> is
> >>>> an uncountable number of RDF* triples.
> >>>>
> >>>> Does this cause  any problems for RDF*?  That I am not sure of.
> >>>>
> >>>>
> >>>> peter
> >
> >
>
>