entailments and the unstar mapping

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