Consistency Is Not Coherence: Orientation Search for Certified Alignments Between 4D Defence Upper Ontologies

Fabio Rovai

Source-linked AI summary

Consistency Is Not Coherence: Orientation Search for Certified Alignments Between 4D Defence Upper Ontologies

Fabio Rovai

arXiv:2608.21914v1Aug 22, 2026cs.AIcs.DBcs.LO

TL;DR

The paper addresses the lack of a public IES–HQDM alignment and the gap between similarity-scored correspondences and logical axioms. It converts a hand-curated 17-correspondence crosswalk into OWL and reasons over complete merged ontologies with HermiT. The results show that consistency can coexist with severe incoherence, while orientation search preserves certified mappings.

Problem
No public IES–HQDM alignment existed, and alignments are often consumed as logical axioms despite being published as similarity-scored correspondences.
Method
The paper promotes a hand-curated 17-correspondence crosswalk to OWL and evaluates complete merged ontologies with deterministic HermiT reasoning and orientation search.
Results
A consistency check misses substantial damage: the 17-correspondence merge adds 100 unsatisfiable classes and 218 conservativity violations, while the conclusion reports 39 native HQDM casualties.
Takeaways & Limitations
Logical alignment evaluation must report input coherence and conservativity, while orientation search can retain expert mappings and certify equivalence or one-directional links.
Takeaways & Limitations
The crosswalk is limited to 17 backbone correspondences, was curated by one author, and orientation search is greedy under a fixed order with ancestor-chain weakening.

Abstract

from arXiv · show

We align three upper ontologies that sit under UK and NATO defence data infrastructure: the Information Exchange Standard (IES), the Higher Quality Data Model (HQDM) that underpins the National Digital Twin, and Basic Formal Ontology (BFO). No public alignment between IES and HQDM existed. Promoting a hand-curated 17-correspondence crosswalk to OWL and reasoning over the complete merged ontologies with HermiT produces three results that we believe matter beyond this pair.

1. Introduction

The paper turns a hand-curated IES–HQDM crosswalk into reasoner-certified OWL axioms and tests what happens when correspondences are treated as logic. It identifies native defects, alignment-induced incoherence, and orientation search as an alternative to deletion.

IES, HQDM, and BFO support UK and NATO-related defence data infrastructure, with IES covering assertions about people, events, and places and HQDM underpinning the National Digital Twin.
No public IES–HQDM alignment existed, while prior IES–BFO work deferred axiomatic translation definitions from plausible semantic equivalence to provable equivalence.
The paper supplies that missing layer by expressing every correspondence as a reasoner-certified OWL axiom.
39 HQDM classes are unsatisfiable natively, so mappings to those classes are vacuously true and semantically empty unless input coherence is reported.
Naive equivalence promotion of the 17-correspondence crosswalk remains consistent but adds 100 unsatisfiable classes and 218 conservativity violations.
Orientation search changes correspondence direction and weakens targets before attempting equivalence, preserving more expert mappings than deletion.

2. Materials and background

The study measures three upper ontologies, defines coherence and conservativity as distinct alignment criteria, and uses a 17-correspondence crosswalk with documented semantic divergences. These distinctions motivate evaluating logical effects rather than relying on consistency or similarity alone.

2.1. The three ontologies: IES contains 511 named classes with zero class-disjointness axioms, HQDM contains 229 named classes and 14 disjointness axioms, and BFO 2020 contains 35 named classes and 19 disjointness axioms.
2.1. The three ontologies: Table 1 measures named classes, disjointness, and native unsatisfiable classes on the vendored files using HermiT ontology by ontology.
2.1. The three ontologies: All IES claims refer to the vendored successor file identified by content hash because repository lineages have different counts.
2.1. The three ontologies: IES and HQDM are four-dimensionalist, whereas BFO separates disjoint continuant and occurrent branches, creating the central difficulty for their join.
2.2. The crosswalk: The crosswalk contains 17 SSSOM correspondences: 13 close matches and 4 related matches recorded as warnings, plus six documented divergences.
2.2. The crosswalk: IES Event corresponds to HQDM activity rather than HQDM event, which is instantaneous and lacks duration and participants.
2.3. Consistency, coherence, conservativity: Consistency permits a model, while coherence requires no named class to be unsatisfiable; therefore consistency does not guarantee meaningful class structure.
2.3. Consistency, coherence, conservativity: Conservativity forbids the merged alignment from entailing new subsumptions between classes of an input ontology.

3. Orientation search

Orientation search replaces deletion-based repair with reasoner-guided choices about correspondence strength and direction. It weakens defective targets, tests reverse edges, and returns a deterministic maximal bridge under explicit coherence and conservativity criteria.

3.1. The operator: Conventional repair removes a minimal diagnosis of mappings, discarding expert correspondences and recording no explanation for failure.
3.1. The operator: Orientation search treats each correspondence’s logical strength as the search variable because SKOS relations do not determine whether the OWL relation should be equivalence or subsumption.
3.1. The operator: When forward subsumption fails because a target is defective, the method weakens the target to an ancestor.
3.1. The operator: P1 accepts forward edges while weakening targets until S1′ or S2 passes, and P2 tests reverse edges before completing surviving pairs to equivalence.
3.1. The operator: The procedure records the reasoner’s witness when a reverse edge fails, providing a justification for one-directionality.
3.1. The operator: The method checks new within-ontology subsumptions in the merged model as conservativity violations.
3.2. Instantiation: HermiT reasons over complete merged ontologies in about two minutes and roughly 35 calls, producing deterministic certified output.
3.2. Instantiation: The relative coherence criterion isolates alignment damage from HQDM’s 39 native casualties, while greedy P2 returns a maximal rather than provably maximum bridge.

4. Results

The complete-ontology experiments separate consistency from coherence: HQDM is defective before alignment, naive equivalence promotion passes consistency while causing extensive incoherence, and orientation search produces a certified bridge that preserves directional information. The BFO experiments show that safe alignment depends on the whole bridge and, in one case, on retargeting rather than weakening.

4.1. The target ontology is broken before we touch it: 39 HQDM classes are unsatisfiable before alignment, concentrated in its relationship-derived branch because OWL disjointness conflicts with EXPRESS relationship semantics.IES and BFO alone have no unsatisfiable classes; the affected HQDM classes include association, employment, ownership, participant, sign, asset, transfer_of_ownership and physical_quantity.
4.2. Consistent, and thoroughly incoherent: Naive equivalence promotion passes the consistency check but adds 100 unsatisfiable classes and 218 conservativity violations to the merged IES–HQDM ontology.The violations include new IES subclass statements such as ies:Entity ⊑ ies:State and ies:Investigation ⊑ ies:State.
4.3. The certified IES↔HQDM bridge: Weakening ies:EventParticipant ⊑ hqdm:participant to ies:EventParticipant ⊑ hqdm:state reduces new unsatisfiability from 100 to 0 because hqdm:participant is the single defective HQDM target involved.Exactly one of the ten class targets, hqdm:participant, is among HQDM’s 39 native casualties.
4.3. The certified IES↔HQDM bridge: Orientation search returns 21 directed axioms with 0 new unsatisfiable classes and 0 conservativity violations; five class pairs and all three property pairs become full equivalences.Four class pairs remain one-directional with reasoner counterexamples, and one is weakened, preserving distinctions where the standards disagree.
4.4. Crossing to BFO: only via the occurrent branch: For IES–BFO, mapping ies:Entity to bfo:material entity makes 101 IES classes unsatisfiable, while retargeting it to bfo:history reduces the count to 0.The result depends on the complete bridge: the bfo:continuant/bfo:occurrent disjointness fires only once the other IES mappings connect the 4D backbone to the occurrent branch.
4.5. The fused three-ontology artifact: The certified IES↔HQDM and IES↔BFO bridges remain jointly safe over IES ∪ HQDM ∪ BFO and admit direct HQDM↔BFO anchors.The union is certified at 0 new unsatisfiable classes and 0 conservativity violations.

5. Do existing systems produce this bridge?

Existing matchers recover only part of the expert bridge and can produce logically unsafe or semantically misleading alignments. LogMap’s repair achieves safety, but orientation search retains substantially more directed content while exposing counterexamples and divergent semantics.

Classical matchers: Both matchers accept ies:Event ≡ hqdm:event, turning a durative happening into an instantaneous boundary and entailing hqdm:activity ⊑ hqdm:event.They also accept mappings to two natively unsatisfiable HQDM classes and map RDF(S) vocabulary.
Classical matchers: LogMap recovers 3 of 10 expert IES–HQDM backbone correspondences and none of the four substantive IES–BFO targets.The backbone correspondences are specifically difficult for lexical matching.
Classical matchers: LogMap’s incomplete internal repair leaves 87 newly unsatisfiable classes after its propositional repair and post-repair checking.The residue measures the gap between scalable projection and complete DL reasoning.
Repair comparison: LogMap’s repair keeps all ten mappings with 0 new unsatisfiable classes and 0 conservativity violations, but uniformly reverses every equivalence.This discards the crosswalk’s forward IES-to-HQDM content.
Repair comparison: Orientation search preserves 21 directed axioms, including five class and three property equivalences, whereas LogMap retains ten uniformly reversed axioms.Both outputs are coherent and conservative, so the distinction is retained logical content at equal safety.
LLM oracle: Both LLMs recover easy lexical mappings but choose hqdm:event for ies:Event and bfo:entity rather than the certified BFO counterpart for ies:Entity.The probe used 12 queries across HQDM and BFO and supports a qualitative error-structure claim, not a significant aggregate comparison.

6. Discussion

The paper argues that alignment evaluation should report input-ontology coherence and preserve correspondence direction, not treat consistency alone as sufficient. It also offers the IES–HQDM material as a candidate defence-alignment test case with repaired and unrepaired references.

Evaluation practice: A matching test case should include a coherence report for each input and flag correspondences targeting unsatisfiable classes.The 39-class HQDM defect was invisible without reasoning over the input ontology alone, and precision or recall on such mappings measures agreement about an empty set.
Alignment representation: Alignment formats should carry direction because subsumption can preserve a useful one-way relation where equivalence falsely identifies standards’ concepts.SSSOM and EDOAL can express directed correspondences, but the paper calls for computing direction rather than defaulting to equivalence.
Relevance to OAEI: The paper’s material has the DISO track’s two-reference structure: an unrepaired consistent but incoherent alignment and a repaired certified bridge explained by counterexamples.The collection currently lacks HQDM, so the IES–HQDM leg is a join the track cannot evaluate.
Relevance to OAEI: The proposed case is small enough for exhaustive reasoner-based evaluation yet adversarial for lexical matchers, combining an exact-label false friend with a correct BFO target sharing no vocabulary.It includes IES, BFO, HQDM, the expert crosswalk, and both reference alignments.

7. Limitations

The paper’s scope and search procedure impose important boundaries: the crosswalk is partial, orientation search is greedy, and weakening cannot re-target across ontology branches. System comparisons and the LLM probe also cover limited configurations and samples.

Scope and evidence: The 17-correspondence crosswalk covers only the 4D backbone, leaving the nonparallel powertype hierarchies unattempted.Its correspondences were hand-curated by one author, with subjective confidence; certification covers logical form, not domain correctness.
Search limitations: Weakening cannot reach a correct target on a different branch because it searches only ancestors of the asserted target.In the BFO ablation, bfo:history is unreachable from bfo:material entity, while the reachable bfo:entity target is safe but uninformative.
Search limitations: Re-targeting remains outside the search, although a target-ontology candidate generator filtered by the same criteria is proposed as the next step.The current completion phase is greedy under a fixed correspondence order, returning a maximal rather than provably maximum bridge.
Evaluation boundaries: The systems comparison used July-2021 LogMap in default configuration, DEBUGGER with only ten class correspondences, and excluded AgreementMakerLight and BERTMap.Tuned or interactive LogMap use might perform better, and extending the comparison is identified as a next experiment.
Evaluation boundaries: The LLM probe comprised 12 queries on two models from one family, supporting qualitative error-structure claims but no quantitative claim.A stronger evaluation would use multiple model families, prompt formats, and a larger candidate pool.

8. Related work

The paper extends established work on incoherence diagnosis, repair, weakening, learned matching, and ontology foundations by certifying alignments among IES, HQDM, and BFO. Its IES–BFO result turns an earlier graph-level pattern into an axiomatic distinction, while its IES–HQDM alignment is presented as the first public one.

Alignment repair: Alignment-incoherence research established coherent alignments as the target and repair as a minimal-hitting-set problem, while LogMap made logic-based repair practical.The paper positions its work within diagnosis-based repair and scalable matching systems.
Alignment repair: The paper applies weakening-and-completing at the alignment layer, changing a mapping target rather than an axiom in either input ontology.This extends axiom-weakening work developed for EL ontologies.
Learning and evaluation: Learned matchers followed by symbolic repair and LLM candidate-generation approaches motivate the paper’s small negative probe of lexical errors.MELT provides the evaluation platform for the OAEI 2026 campaign and its DISO track.
Ontology foundations: HQDM, BFO, and IES derive from established ontology and data-modelling traditions, while prior census work found inadequate exclusion structure in IES and HQDM.This paper instead examines what their declared axioms do to one another when merged.
IES–BFO alignment: Earlier IES–BFO work proposed a graph-level pattern linking an IES4 4D individual to a BFO material entity and its history.The present certified bridge retains ies:Entity ⊑ bfo:history but not bfo:material entity, and supplies the previously deferred axiomatic layer.

9. Conclusion

The conclusion shows that consistency checks alone can miss severe alignment damage, while orientation search can preserve expert correspondences through certified directional links and equivalences. The BFO case further identifies the occurrent branch as the route for crossing its 3D core.

9. Conclusion: Two upper ontologies aligned over 17 backbone correspondences pass consistency checking yet produce 100 new unsatisfiable classes, while HQDM already contains 39 native casualties.These defects are invisible without reasoning and absent from similarity scores.
9. Conclusion: Orientation search treats correspondence direction as the variable and uses a prover to check coherence and conservativity at each step.It preserves every expert mapping, uses equivalence where supported, and adds machine-found counterexamples where standards diverge.
9. Conclusion: No tested system recovered the certified bridge: matchers accepted a false friend, while the successful repair discarded every provable equivalence.For BFO, the 4D entity crosses its 3D core through the occurrent branch because it is a continuant’s history, not the continuant itself.

Declaration on Generative AI

The author used Anthropic Claude for drafting, literature triage, and LaTeX preparation, while separately evaluating locally served Qwen3-Coder-30B models. The author states that experiments and reported results were independently designed, executed, verified, and reviewed.

Declaration on Generative AI: Anthropic Claude assisted with drafting and revising text, literature triage, and LaTeX preparation.The locally served Qwen3-Coder-30B models were systems under evaluation, not writing tools.
Declaration on Generative AI: The author states that all experiments, reported numbers, and reasoner runs were designed, executed, and verified by the author.The author also reviewed and edited the content and takes responsibility for the publication’s content.

A. Data and code availability

The crosswalk, supporting artifacts, evaluation outputs, and benchmark are publicly released under CC-BY-4.0, with reproduction enabled by the provided orientation-search script.

A. Data and code availability: The crosswalk and associated divergence, SHACL, orientation-search, bridge, and decision-log artifacts are released under CC-BY-4.0.The release includes SSSOM, SKOS/PROV-O, three certified bridges, and full decision/counterexample logs.
A. Data and code availability: The repository includes LogMap and LogMapLt outputs, an evaluation harness, and an LLM benchmark.The evaluation harness contains reasoning/systems/ and systems_eval.py.
A. Data and code availability: The results reproduce with python reasoning/orientation_search.py given any JDK, using publicly available input ontologies.IES is licensed under OGL v3 and HQDM under Apache-2.0.