Re: how many RDF* triples?

On 15/10/2020 11:55, Jos De Roo wrote:

> 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

to me, this is exactly the example that Peter proposed initially --
unless I am missing something...

>
> -- 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
> <mailto: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
>     <mailto: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
>     >
>     >
>