Semantics Proposals

There have been several proposals for a model-theoretic semantics for RDF-star.

There is the community group proposal in https://www.w3.org/2021/12/rdf-star.html#rdf-star-semantics In this semantics, quoted triples exist in interpretations as resources that are related to their subject, property, and object by unstar:subject, unstar:predicate, unstar:object and also related to the syntax of their subject, property, and object (except for blank nodes) by other properties. There is no requirement that there is only one resource with the same unstar:subject, unstar:object, and unstar:predicate. IRIs in the unstar: vocabulary cannot appear directly in RDF graphs. (Actually they can appear but they are mapped to different properties.) Quoted triples in a graph are injectively mapped into these unstructured resources. This semantics is semi-transparent, in that the syntactic form of subjects, predicates, and objects are significant except for blank nodes. The treatment maps through blank nodes to achieve transparency and uses the syntactic properties to defeat transparency except for blank nodes.

There is a proposal from Enrico Franconi in https://lists.w3.org/Archives/Public/public-rdf-star-wg/2023Feb/0084.html In this proposal there is an extra mapping from 3-tuples of resources to resources. Quoted triples are mapped to resources by first mapping their subject, predicate, and object to resources then using this extra mapping.
Because the mapping goes through the referrent of the subject, predicate, and object the semantics is fully transparent.

There is a proposal from Antoine Zimmermann in https://www.emse.fr/~zimmermann/W3C/RDF-star-semantics/ In this proposal, quoted triples exist in interpretations as resources that are related to their subject, property, and object by special properties that are the denotation of rdf:subject, rdf:predicate, and rdf:object. There is no requirement that there be only one resource with the same values for rdf:subject, rdf:predicate, and rdf:object. Quoted triples are directly mapped into these resources. This semantics is non-transparent because of the direct mapping from quoted triples to resources.

There is a proposal from several members of the working group that has been discussed privately. This proposal has not been written down.