Re: how many RDF* triples?

None of these are RDF triples.  They are each shorthand for several RDF
triples.   The first is

_:a _p _:l1 .

_:l1 rdf:first _:a .

_:l1 rdf:rest _:l2 .

_:l2 rdf:first :p .

_:l2 rdf:rest rdf:nil .


The entire thing is a countably infinite number of triples.



I used the wrong term in my original message.  I used "element" when I should
have used "constituent".  RDF* triples have constituents.  As sets, RDF and
RDF* graphs have elements.


peter




On 10/15/20 7:29 AM, Jos De Roo wrote:
> It was intended as shorthand for
>
> @prefix : <http://example.org/test# <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
> <mailto: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
>     <mailto:pierre-antoine.champin@ercim.eu>>
>     To: Jos De Roo <josderoo@gmail.com <mailto:josderoo@gmail.com>>
>     Cc: public-rdf-star@w3.org <mailto: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/ <https://josd.github.io/>
>     <http://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>
>     > <mailto: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>
>     >     <mailto: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/
>     <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
>     >     >
>     >     >
>     >
>

Received on Thursday, 15 October 2020 12:42:38 UTC