Round-Trippable RDF 1.2 Interoperability

This article is positioned in the work around triple terms within the upcoming RDF 1.2 specification.
Concretely, the authors are concerned around the problem of interoperability to systems that do not support triple terms.
For this, the authors rely on a bidirectional conversion algorithm to go from RDF 1.2 with triple terms to RDF 1.2 without term terms,
from the RDF 1.2 Interoperability spec (created by the same authors).
The authors formally ground triple terms and this conversion, provide proofs, and carry out an empirical study.

In general, I consider this work useful and well carried out.
It could be argued that this work is quite straightforward, especially the findings on the blow-up of triples after conversion.
But the formal grounding of this work will be a useful foundation for future papers to build upon.
Besides several minor issues, I'm of the opinion that this work should be accepted.

For disclosure, I am involved in the RDF & SPARQL working group together with the authors of this article. I have not been involved in work around the RDF 1.2 Interoperability specification. That means I have the necessary background to assess this article, without having a conflict of interest.

## Strengths

S1. RDF 1.2 interoperability is a timely and relevant topic
S2. The paper is well written and easy to understand
S3. The authors provide an open-source implementation of their conversion tool, with reproducible experiments.

## Weaknesses

W1. Unclear why a new vocabulary is used instead of the old-style reification vocabulary

I could not find in the paper a motivation as to why the authors created a new vocabulary,
instead of just using the existing reification vocabulary, which is functionally equivalent.
Eventually, I found a reasoning for this in the actual spec.
But for self-containedness, I would recommend explaining this in the paper directly.

W2. The impact on specific RDF processors is not analyzed

While the authors performed various empirical experiments around the dataset size increase and encoding/decoding runtime overhead,
the impact on real-world processors (e.g. SPARQL query engines, SHACL validators, rule engines, ...) is not discussed or analyzed.
The authors do however mention this as future work at the end of the paper.
I am just listing this as a minor weakness that could make this work stronger,
but I understand that this is not in scope of the aims of this work here.

## Minor issues

- Page 1: Introduction: When the authors talk about "individual assertions", I would recommend adding a concrete use case, for example using some visualization. Some high-level use cases are mentioned (provenance, evidence, confidence, qualifiers, attribution, temporal validity, and change tracking), but it remains fuzzy. For readers that are not familiar yet with statement-level annotations, the motivation for this paper would become clearer that way.
- Page 3: Typo: "if it is not a blank nodes."
- Page 4: Section 3.2.1: For the sake of completeness, it would be good to write out the URL to which the prefix rdf refers to.
- Page 12: When talking about named graphs, it would also be relevant to mention the fact that named graph semantics are unclear. Different people use them for different purposes, which are often incompatible, which leads to data integration issues.
- Page 12: When RDF-star is discussed, it would be good to mention that RDF-star acted as starting point for the RDF & SPARQL working group, which ended up as RDF 1.2.
- Page 12: Given the strong relation between RDF-star and RDF 1.2, I would recommend also adding related work around RDF-star, such as:
- Taelman, Ruben, and Ruben Verborgh. "In-memory dictionary-based indexing of quoted RDF triples." 7th Workshop on Storing, Querying and Benchmarking Knowledge Graphs (QuWeDa) at ISWC 2023. Vol. 3565. 2023.
(Yes, that's my paper. It's especially relevant given the focus on "depth" on query/indexing performance.)
- Delva, Thomas, et al. "RML-star: A declarative mapping language for RDF-star generation." Proceedings of the ISWC 2021 Posters, Demos and Industry Tracks: From Novel Ideas to Industrial Practice 2980 (2021).
- Arenas-Guerrero, Julián, et al. "Declarative generation of RDF-star graphs from heterogeneous data." Semantic Web 16.2 (2025): SW-243602.
- Egami, Shusaku, et al. "RDF-star2vec: RDF-star graph embeddings for data mining." IEEE Access 11 (2023): 142030-142042.
- Abuoda, Ghadeer, et al. "Transforming RDF-star to Property Graphs: A Preliminary Analysis of Transformation Approaches." QuWeDa@ ISWC. 2022.
- Abouda, Ghadeer, et al. "StarBench: Benchmarking RDF-star triplestores."

This paper formalizes the interoperability transformations between the two RDF 1.2 conformance profiles: RDF 1.2 Full and RDF 1.2 Basic. The authors present a basic encoding (Full to Basic) that replaces each triple term with a fresh blank node and records its components using a reserved reification vocabulary (rdf:PropositionForm), and a corresponding basic decoding (Basic to Full) that reverses this. The transformations are grounded in the RDF 1.2 abstract syntax and model-theoretic semantics. The paper establishes correctness properties (invertibility and idempotence) under explicit admissibility conditions, and clarifies the semantic status of the transformations under standard RDF semantics. An experimental study complements the formal results, evaluating structural overhead, runtime scalability, and robustness on synthetic benchmarks and a real-world case study.

The paper is closely tied to the W3C Group Note Draft "RDF 1.2 Interoperability" and serves as its mathematical companion. One of the authors (Champin) is co-editor of the W3C working drafts, lending the work direct practical relevance.

Strengths

1. Timely and directly relevant. RDF 1.2 is actively being standardised, and the interoperability between Full and Basic profiles is a concrete practical problem.

2. Clean formal development. The paper is mathematically precise.

3. Semantic clarification. Section 4, together with the discussion in the conclusion, clarifies an important point: the transformations preserve syntactic structure rather than entailment.

4. Comprehensive experimental evaluation, robustness testing, anf good resource availability.

Questions

Would it be possible to encode/decode incrementally? The conclusion briefly mentions "streaming or incremental algorithms for large-scale datasets" as future work. Can we apply these encoding/decodings on an stream?

Data and Resources Assessment

The resources are well organized. The software is archived on Zenodo, which is appropiated for long-term preservation. The provided resources appear complete.

This paper addresses the problem of RDF 1.2 full and basic interoperability providing a formal account of the transformations proposed in a W3C group note. It formalizes the encoding and decoding of graphs and datasets, from Full to BAsic, and back. The topic is relevant, supporting the work done arounf RDF 1.2 and its upcoming Recommendation release, and the overall structure is sound. Next, I provide some comments that I hope will improve the paper, some of them requiring special attention before publication.

# Semantic definitions and the core contribution
The semantic apparatus of section 2.2 is developed entirely for GROUND expressions, yet the encoding/decoding approach in section 3 is fundamentally built around fresh blank nodes, which are non-ground terms. The authors should clarify why these semantic definitions are relevant. Without this clarification, the reader is left wondering why ground semantics are developed when the core contribution operates entirely on non-ground graphs.

# Definition 3.2 (encoding-admissible graphs) seems insufficient
The admissibility condition only checks triples of the form "b--rdf:type--rdf:PropositionForm". However, if the input graph already contains triples using any of the other reserved predicates with a blank node subject, the uniqueness condition (D1) of definition 3.14 may be violated after encoding, breaking decoding admissibility and thus the round trip guarantee of theorem 4.1. In my view, the admissibility condition should be strengthened to exclude all four reserved vocabulary terms from appearing with blank node subjects in the input graph

# Running example
The paper introduces a large number of definitions in rapid succession, many of which are highly technical and interdependent. A simplified running example illustrating the definitions would significantly improve readability. I encourage the authors to consider adding this running example if they also think it would help to follow the paper more easily.

#### EVALUATION COMMENTS ####
# Hardware environment not specified
The paper does not report the hardware used for experiments (CPU, RAM, operating system, Python version)

# Statistical methodology underspecified
The paper repeatedly refers to "multiple runs" and "median" measurements without specifying the number of runs performed. The authors should state the exact number of repetitions

# Reuse factor is not formally defined
The reuse factor is described informally as controlling the number of distinct triple terms, but the paper never provides a precise formula relating u, r and N, and the number of unique triple terms.

# Round trip correctness (EQ1) should not be presented as an empirical finding
The observation that decoding the basic encoding yields the original full graph is a direct consequence of theorem 4.1, which is formally proved in section 4. Confirming a mathematical theorem experimentally adds no scientific value. The authors should reframe EQ1 explicitly as an implementation validation (confirming that the code correctly realizes the formal specification) rather than as an experimental result.

# The 4U structural overhead rule is not a finding
The repeated use of "approximately", "about", and "≈" when describing the structural overhead ΔT=4U is incorrect and misleading. This relationship is exact by construction (definition 3.3 introduces precisely four triples per unique triple term), as the authors themselves confirm in the YAGO4 case study. Furthermore, the 4U rule is presented as if it were a surprising experimental finding, but it follows trivially and directly from definition 3.3. The experiments are only meaningful for measuring runtime scaling behaviour. The structural overhead is a mathematical certainty that requires no experimental verification. The authors should remove the approximation language and should not present the 4U rule as a result.

# No comparison to alternative encodings
The paper positions the basic encoding as one possible interoperability strategy among several. However, the experimental section provides no comparison against these alternatives. It would significantly strengthen the contribution to include an evaluation showing whether and to what extent the proposed encoding compares favourably to other approaches such as standard reification or singleton properties in terms of structural overhead and runtime. This comparison would have evidenced the practical advantages of the approach wrt other alternatives, and maybe this could be added as future work.