Re: entailments and the unstar mapping

Hi Pierre-Antoine,
Your example emphasises exactly my point of never allowing a RDF-star graph to contain unstar: predicates. In my view, unstar: predicates are only useful to suggest an easy but sound and complete  implementation of RDF-star entailments via RDF-1.1 simple entailment. Roughly speaking, an RDF-star triple T is RDF-star entailed by RDF-star graph G if and only if L(G) RDF-1.1 simply entails L(T). Notice that the game changes already for extensions such just adding owl:sameas, where the above is not true anymore.
Cheers
—e.

On 20 Mar 2023, at 10:56, Pierre-Antoine Champin <pierre-antoine@w3.org> wrote:



Hi Enrico,

during our conversation last Friday, I promised a discussion about the unstar mapping defined in the CG Report  (https://www.w3.org/2021/12/rdf-star.html#dfn-unstar).

What you said (or at least what I understand you said) was: given an RDF-star graph G, G and unstar(G) have the same entailments. I disagree with this assertion (see 1 below), but I agree with a weaker version of this assertion (see 2 below).


1. I disagree with the assertion

Consider the following RDF-star graph G (serialized in Turtle, assuming the appropriate prefix declarations):

    ex:a unstar:subject ex:b.

unstar(G) is the following:

    ex:a unstar:subject_ ex:b.  # notice the underscore at the end of the predicate

which entails G'

    ex:a unstar:subject_ [].

unstar(G) entails G', however, G does not entail G'!

On the other hand, consider the RDF-star graph H:

    ex:a unstar:subject [].

We can see that unstar(H) = G'
(that is, assuming that "[]" in both Turtle sources refer to the *same blank node*)

Since unstar(G) entails unstar(H), it follows that G entails H. However, unstar(G) does not entail H.

So G and unstar(G) both entail a graph that is not entailed by the other.


2. I agree with a weaker version of the assertion

Granted, my examples above are somewhat pathological, because I use the 'unstar:' vocabulary in the RDF-star graph. Since we want to avoid nasty interactions with this kind of pathological triples and the triples produced by the unstar mapping, we use a form of escaping, which is why, in my counterexample above, G and unstar(G) have different entailments.

If we restrict ourselves to "nice" RDF-star graphs, i.e. RDF-star graphs that do not use the 'unstar:' vocabulary, then we can assert :

  for any "nice" RDF-star graph G containing no quoted triple, then G = unstar(G)
  (and therefore G and unstar(G) have the same entailments!)

Note that, for any "nice" RDF-star graph that contains some quoted tripes, there are some entailments of unstar(G) that are not entailedby G. E.g., unstar(G) will always entail

  [] unstar:subject [] .

while G will not (because, being nice, it contains no triple with predicate unstar:subject).

Note also that there are also some entailments of G that are not entailed by unstar(G). For example, G entails itself, while unstar(G) can not entail anything that contains quoted triples (being an RDF 1.1 graph).

  best




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