Re: how many RDF* triples?

It was intended as shorthand for

@prefix : <http://example.org/test#>.

_:a :p (_:a :p ()).
_:a :p (_:a :p (_:a :p ())).
_:a :p (_:a :p (_:a :p (_:a :p ()))).
_:a :p (_:a :p (_:a :p (_:a :p (_:a :p ())))).
_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p ()))))).
_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p ())))))).
_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p (_:a :p ()))))))).
...

which is perfect RDF

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


On Thu, Oct 15, 2020 at 1:17 PM Olaf Hartig <olaf.hartig@liu.se> wrote:

> Jos, this is neither an RDF triple nor an RDF* triple. What is "..."?
>
> Olaf
>
> -----Original Message-----
> From: Pierre-Antoine Champin <pierre-antoine.champin@ercim.eu>
> To: Jos De Roo <josderoo@gmail.com>
> Cc: public-rdf-star@w3.org
> Sent: Thu, 15 Oct 2020 12:54
> Subject: 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
> >     >
> >     >
> >
>