Re: Semantic Predication: 4 - more worked out examples

[And I understand now that your proposal is to enable users to make
this intention explicit by giving them two different forms of
embedded triples (or even a third form for the modal /epistemic
predication).

Indeed :-)

Okay :-)

Now, assuming that we decide to go in this direction, we need such a sy
ntactic distinction between different kinds of embedded triples not
only for a particular serialization format such a Turtle or N-Tripels,
but we actually need a way to capture this distinction directly in the
formal/abstract syntax of the data model itself. I am referring to the
notion of an RDF-star triple as defined at:
https://w3c.github.io/rdf-star/cg-spec/2021-12-17.html#dfn-triple

Therefore, my next question then is: Do you also have a proposal for
how the syntactic distinction between different kinds of embedded
triples can be captured in the formal/abstract syntax of the RDF/RDF-
star data model?

This requires a change to the RDF Concepts and Abstract Syntax document, which defines the abstract syntax (a data model) which serves to link all RDF-based languages and specifications. This is needed anyway, even if RDF-star introduces just one type (as opposed to multiple types) of embedded triples.
Currently, the RDF 1.2 Concepts and Abstract Syntax document says:
"There can be three kinds of nodes in an RDF graph: IRIs, literals, and blank nodes."
EDITOR'S NOTE: Four kinds of nodes now, including quoted triples.
Obviously, there will be more than one type of quoted triple.

In the current RDF-star CG final report:
any RDF triple is an RDF-star triple;
if t and t' are RDF-star triples<https://w3c.github.io/rdf-star/cg-spec/2021-12-17.html#dfn-triple>, s is an IRI<https://www.w3.org/TR/rdf11-concepts/#dfn-iri> or a blank node<https://www.w3.org/TR/rdf11-concepts/#dfn-blank-node>, p is an IRI<https://www.w3.org/TR/rdf11-concepts/#dfn-iri>, o is an IRI<https://www.w3.org/TR/rdf11-concepts/#dfn-iri>, a blank node<https://www.w3.org/TR/rdf11-concepts/#dfn-blank-node> or a literal<https://www.w3.org/TR/rdf11-concepts/#dfn-literal>, then (t, p, o), (s, p, t) and (t, p, t') are RDF-star triples<https://w3c.github.io/rdf-star/cg-spec/2021-12-17.html#dfn-triple>.
Here we could introduce three abstract notations (…), ((…)), (((…))) for RDF-star embedded triples. And so on.

Probably a way to simplify the presentation could be to say upfront that, according to the semantics of RDF-star, any RDF-star graph is logically equivalent to some RDF 1.1 graph, according to the model theoretic semantics of RDF-star (see my Semantic Predication: 5 - model theory message), which monotonically and compositionally extends the semantics of RDF 1.1.

cheers
—e.