RDF-Specialization.md

Extension: Specialization to Signed RDF Graphs

RDF graph payload

Assume that the content identifier $\mathsf{body}(B) \in \mathcal{C}$ references a concrete RDF graph: $\mathsf{G}(B) \subseteq \mathcal{T}$ where $\mathcal{T}$ is the set of RDF triples of the form $(s, p, o)$.

We interpret $\mathsf{G}(B)$ as the payload graph authored by $\mathsf{issuer}(B)$.

Reification

We define a reification function $\mathsf{reify}(B)$ that maps the signed graph to a named graph or quads with provenance.

For each triple $t \in \mathsf{G}(B)$, define the reified form:

$$ \mathsf{reify}(B) = { (s, p, o, g_B) \mid (s, p, o) \in \mathsf{G}(B) } $$

where $g\_B \in \mathcal{U}$ is a unique graph name associated with the block $B$, such as:

$$ g_B := \texttt{did:} \mathsf{issuer}(B) \# \mathsf{id}(B) $$

Alternatively, if using RDF-star or PROV-O, the reification can instead be:

• A named graph or blank node denoting the assertion
• Annotated with:
  • $\texttt{prov:wasAttributedTo} \ \mathsf{issuer}(B)$
  • $\texttt{prov:wasDerivedFrom} \ \mathsf{id}(B)$

The exact form depends on the RDF dialect used, but semantically the payload is treated as authored assertions by the signer.

State computation

Given a participant $u$, let $\mathcal{V}_u$ be the set of blocks visible under subjective traversal (see prior section with accept/reject logic).

Define the participant’s assembled state graph $\mathsf{S}_u$ as:

$$ \mathsf{S}_u := \bigcup_{B \in \mathcal{V}_u} \mathsf{reify}(B) $$

That is, the total RDF graph is the union of all reified block payloads visible under $u$'s trust and traversal policy.

If RDF-star is used, this could equivalently be:

$$ \mathsf{S}_u := \bigcup_{B \in \mathcal{V}_u} \left\{ \ll t \gg \ \mathsf{prov:wasAttributedTo} \ \mathsf{issuer}(B) \right\} \quad \text{for each } t \in \mathsf{G}(B) $$

Conflict handling

If blocks in $\mathcal{V}_u$ make conflicting assertions (e.g., two blocks claim different values for the same triple), this is not a protocol error — the provenance-aware model allows:

• Leaving conflicting assertions coexisting with different graph names
• Using downstream logic to resolve (e.g., trust-weighted resolution, query filtering)

Thus, state is:

• Provenance-rich: all facts have authorship
• Non-authoritative: clients determine what to trust or prioritize

Summary

Concept	Description
$\mathsf{G}(B)$	RDF graph payload of block $B$
$\mathsf{reify}(B)$	Provenance-aware named graph or RDF-star reification
$\mathsf{S}_u$	State for participant $u$: union of all reified payloads of visible blocks
Conflicts	Allowed; resolution is subjective and external