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

1. Native-defect finding

• The published hqdm.owl contains 39 natively unsatisfiable classes, hidden from its asserted hierarchy and a consistency check, making mappings onto them vacuously true.Evaluating an alignment into HQDM therefore measures against a defective target.Source: §1 · p. 2

2. Separation result on real data

• Naive equivalence promotion of the 17-correspondence crosswalk remained consistent but added 100 unsatisfiable classes and 218 conservativity violations.Exactly one of ten class targets was natively unsatisfiable; weakening that correspondence reduced new unsatisfiability from 100 to 0.Source: §1 · p. 2

3. Orientation search

• Orientation search changes correspondence direction rather than presence, weakening equivalences to subsumptions before attempting completion back toward equivalence.A reasoner checks coherence and conservativity at each step, and rejected directions retain counterexamples documenting disagreements between the criteria.Source: §1 · p. 2

4. Certified bridges

• Three certified bridges, including a 21-axiom IES↔HQDM bridge, achieved zero new unsatisfiable classes and zero conservativity violations across the complete ontologies.The set also includes a hand-specified, certified IES↔BFO bridge and their union with direct HQDM↔BFO anchors. An ablation shows the BFO problem came from targeting the wrong class, not from an overly strong mapping.Source: §1 · p. 2

5. Systems comparison

• LogMap and LogMapLt accepted the false friend, mapped onto natively unsatisfiable classes, and added 87 and 214 unsatisfiable classes plus over a hundred conservativity violations each.With expert input, LogMap returned a certifiably safe but uniformly reversed repair that lost all five provable equivalences. The LLM oracle scored 6/12 on the base model and 7/12 on the IES fine-tune; classical and neural systems failed on the same lexically misleading pairs.Source: §1 · p. 2

2.1. The three ontologies

• IES has 511 named classes and no class-disjointness axioms, HQDM has 229 classes and 14 disjointness axioms, while BFO has 35 classes and 19 disjointness axioms.IES and HQDM are four-dimensionalist, whereas BFO is three-dimensionalist and disjoins continuants from occurrents; the paper says that disjointness makes the IES-to-BFO join crossable only in one place (§4.4).Source: §2.1 · pp. 2–3, Table 1 · p. 3

2.2. The crosswalk

• The hand-curated SSSOM crosswalk contains 17 correspondences: 13 close matches and four related-match warnings, alongside six documented divergences.One divergence is ies:Event, a durative happening, versus hqdm:event, an instantaneous boundary; hqdm:activity is the true counterpart of ies:Event.Source: §2.2 · p. 3

2.3. Consistency, coherence, conservativity

• Consistency requires a model, coherence requires no named class to be unsatisfiable, and conservativity forbids new within-ontology subsumptions caused by the merge.The authors call consistency useless here; their relative-coherence criterion excludes pre-existing unsatisfiable classes because HQDM has 39 native casualties, while the conservativity criterion bars new same-ontology subsumptions.Source: §2.3 · pp. 3–4

3.1. The operator

• Rather than delete mappings that break coherence, orientation search reconsiders their logical strength, which a SKOS crosswalk does not specify.The approach aims to preserve expert-asserted correspondences while recording why a relation cannot be strengthened.Source: §3.1 · p. 4
• When forward subsumption still fails because a target is defective, the search can weaken the target to an ancestor, following axiom weakening.This adds a fifth move to the relation-strength search.Source: §3.1 · p. 4
• P1 weakens failing forward edges upward, then P2 greedily tests reverse edges; surviving pairs become equivalences, while others remain one-directional with a reasoner witness.The output links the standards bidirectionally where they agree and in one direction where they do not.Source: §3.1 · p. 4

3.2. Instantiation

• HermiT via owlready2 checks the complete merged ontologies in about 35 reasoner calls and two minutes on a laptop, producing deterministic certified output.HermiT is used as a description-logic prover without a learned component.Source: §3.2 · p. 5
• Relative S1′ isolates alignment-caused damage from HQDM’s 39 native casualties; greedy P2 yields a maximal, not provably maximum, certified bridge under a fixed correspondence order.Every output axiom is individually certified regardless of order.Source: §3.2 · p. 5

4.1. The target ontology is broken before we touch it

• HQDM alone has 39 unsatisfiable classes, concentrated in its relationship-derived branch, where first-class EXPRESS relationships collide with OWL-rendered disjointness axioms.Mappings to those classes have empty targets, so the authors recommend coherence reports for each input ontology alongside class and property counts.Source: §4.1 · p. 5

4.2. Consistent, and thoroughly incoherent

• Naive equivalence promotion passes the consistency check but leaves 100 IES operational classes unsatisfiable and creates 218 conservativity violations.The single edge from ies:EventParticipant to hqdm:participant connects IES to HQDM’s defective branch; replacing it with an edge to hqdm:state reduces new unsatisfiability from 100 to 0.Source: Table 2 · p. 5, §4.2 · pp. 5–6

4.3. The certified IES↔HQDM bridge

• 21 directed axioms yield 0 new unsatisfiable classes and 0 conservativity violations; five class pairs and all three property pairs are equivalent, while four class pairs stay directional and one is weakened.Where the standards agree, the bridge uses full equivalence; where they disagree, it retains the weaker relation supported by the reasoner.Source: §4.3 · pp. 6–7, Table 3 · p. 6
• The rejected reverse edges expose specific disagreements: equating IES Entity with HQDM individual forces events under Entity, while the period mappings collapse distinctions IES preserves.The Entity–individual reverse produces 104 violations, including Arrest under Entity; other witnesses force PossibleWorld under PeriodOfTime or collapse the distinction between a period and a particular period.Source: §4.3 · pp. 6–7

4.4. Crossing to BFO: only via the occurrent branch

• Changing the IES Entity mapping from BFO material entity to BFO history reduces unsatisfiable IES classes from 101 to 0, whereas weakening the former mapping still leaves 100 unsatisfiable classes.The other three bridge axioms are held fixed; history is the 4D object on BFO’s occurrent branch, and cwb:hasHistory links it to the continuant.Source: §4.4 · pp. 7–8, Table 4 · p. 7

4.5. All three in one artifact

• The union of the IES↔HQDM and IES↔BFO bridges is certified over all three ontologies at 0 new unsatisfiable classes and 0 conservativity violations, with direct HQDM↔BFO anchors added.The fused artifact contains 32 subsumption axioms and the cwb:hasHistory declaration; hqdm:participant is excluded because it is natively unsatisfiable.Source: §4.5 · p. 8

5.1. Classical matchers on the pair

• LogMap recovers 3 of 10 IES–HQDM backbone correspondences and none for IES–BFO, while both matchers accept the false-friend Event–event mapping.Both also accept mappings to natively unsatisfiable HQDM classes and RDF(S) vocabulary; LogMap’s internal repair leaves 87 new unsatisfiable classes. The authors frame discovery as harder than certifying the expert crosswalk, not as evidence of outmatching matchers.Source: §5.1 · pp. 8–9, Table 5 · p. 9

5.2. LogMap’s repair facility versus orientation search

• At equal safety, LogMap retains 10 uniformly reversed axioms, while orientation search retains 21 directed axioms, including five class and three property equivalences.Orientation search preserves the expert’s forward direction wherever safe and attaches a counterexample to every refusal; LogMap drops the forward edges, keeps a semantically wrong direction on divergent pairs, and retains a mapping onto a provably empty class.Source: §5.2 · p. 9

5.3. An LLM oracle

• Both LLMs choose hqdm:event for ies:Event and bfo:entity rather than bfo:history for ies:Entity, but recover several easy mappings.The probe covers 12 queries; its aggregate is uninformative at this sample size, and the authors claim no significant difference between systems. They describe LLMs as candidate generators but poor adjudicators of upper-ontology disagreement, not as having established a benchmark result.Source: §5.3 · p. 10

• A 39-class defect in hqdm.owl was detectable only by reasoning over the input alone, motivating coherence reports for each input and flags for unsatisfiable correspondence targets.Precision and recall over flagged correspondences measure agreement about the empty set.Source: §6 · p. 10
• Alignment formats should preserve direction because standards often relate through subclass inclusion rather than equivalence, and orientation search can compute that logical strength.SSSOM and EDOAL can express directed correspondences, but computing direction rather than defaulting to equivalence is the missing practice.Source: §6 · p. 10
• The IES–HQDM materials are a candidate DISO test case, pairing an unrepaired crosswalk with a repaired, directed reference alignment.The naively promoted crosswalk is consistent but incoherent, with 218 conservativity violations; the certified bridge explains the delta through machine-found counterexamples. DISO evaluates defence, intelligence and security alignments using repaired and unrepaired references, but its collection lacks HQDM, so it cannot currently evaluate the IES–HQDM leg; the proposed directed reference also supports scoring logical strength using justifying counterexamples.Source: §6 · p. 11

7. Limitations

• The 17-correspondence crosswalk is only a 4D backbone, its hand-curated confidences are subjective, and greedy completion returns a maximal—not provably maximum—bridge.Above the backbone, powertype hierarchies cease to be parallel; P1 also walks a single ancestor chain rather than the full weakening lattice, and certification establishes logical form, not domain correctness.Source: §7 · p. 11
• Weakening cannot reach a correct target on a different branch: from bfo:material entity it reaches only bfo:entity, while bfo:history is unreachable.The four BFO targets were supplied by hand; retargeting within the search using a candidate generator filtered by the same criteria is proposed as future work.Source: §7 · p. 11
• The comparison used default standalone LogMap and DEBUGGER with only ten class correspondences; AgreementMakerLight and BERTMap [10] were not run.Tuned or interactive LogMap might do better; DEBUGGER was not given the three property mappings, and conservativity-repair algorithms [5] remain for future comparison.Source: §7 · p. 11
• 12 queries on two models from one family support only a qualitative claim about error structure, not a quantitative claim.A fuller probe would cover multiple model families and prompt formats, with a candidate pool large enough for Hits@𝑘 to be meaningful.Source: §7 · p. 11
• HermiT was the only reasoner; direct command-line rechecks matched exactly, but this checks the harness rather than providing an independent prover.The counts were IES alone 0, HQDM alone 39, IES+HQDM with the certified bridge 39 with the identical set, and IES+BFO with the certified bridge 0; agreement with a second reasoner would strengthen the certificates.Source: §7 · p. 11

8. Related work

• Unlike incoherence repair and LogMap’s mapping removal or weakening, this method preserves curated correspondences and repairs by direction, completing toward equivalence and recording counterexamples for refusals.The paper argues that the resulting repair log documents disagreements between government standards.Source: §8 · p. 12
• Incoherence diagnosis and minimal-hitting-set repair, scalable logic-based repair in LogMap, and conservativity violation repair [5] provide antecedents; conservative extensions and safe ontology reuse ground the second criterion.Here, repair follows expert commitment to the correspondences, leaving their direction as the variable.Source: §8 · p. 12
• P1+P2 adapts axiom weakening and Li and Lambrix’s [20] weakening-and-completing for EL ontologies to alignment targets rather than axioms in either input ontology.Source: §8 · p. 12
• BERTMap [10] established learned matching followed by symbolic repair, while recent work uses LLMs as candidate generators or oracles [11]; the paper’s §5.3 probe is a negative datapoint for the oracle role when lexical evidence misleads.MELT is the evaluation platform for OAEI 2026, including the DISO track motivating §6.Source: §8 · p. 12
• HQDM derives from West’s data-modelling work in the BORO tradition, while BFO is described in and standardised as; a public-ontology census found neither IES nor HQDM declares exclusion structure adequate for counterfactual reasoning.This paper asks what their declared axioms do to each other when joined.Source: §8 · p. 12
• The bridge is the first certified alignment involving IES and the first public IES–HQDM alignment; of Bailey et al.’s two mapping legs, only ies:Entity under bfo:history survives, not bfo:material entity.The paper presents this as the axiomatic, provable-alignment step deferred by Bailey et al..Source: §8 · p. 12
• The earlier JC3IEDM-to-IES crosswalk was a SKOS-level sketch without reasoner checking; Euzenat and Shvaiko remains the reference text.Source: §8 · p. 12

9. Conclusion

• A hundred operational classes are killed by the consistent merge, while one ontology already killed 39 of its own before alignment.These consequences are detectable by a reasoner but invisible without one and absent from similarity scores.Source: §9 · p. 12
• Orientation search returns a bridge retaining every expert mapping, asserting equivalence where standards agree, and attaching machine-found counterexamples where they do not.It treats correspondence direction as the search variable and uses a prover to check coherence and conservativity at each step.Source: §9 · p. 12
• No tested system recovers the bridge: matchers accept the false friend, while the successful repair discards every provable equivalence.Source: §9 · p. 12
• BFO’s 3D core is crossable only through the occurrent branch: a 4D entity is a continuant’s history, not the continuant.Source: §9 · p. 12

Declaration on Generative AI

• Claude assisted with drafting and revising text, literature triage, and LaTeX preparation.The author reviewed and edited the content after using the tool.Source: Declaration on Generative AI · p. 13
• The locally served Qwen3-Coder-30B models in Section 5.3 were evaluation systems, not writing tools.Source: Declaration on Generative AI · p. 13
• The author designed, executed, and verified all experiments, reported numbers, and reasoner runs, and takes full responsibility for the publication’s content.Source: Declaration on Generative AI · p. 13

A. Data and code availability

• The crosswalk, divergences, SHACL shapes, orientation search, certified bridges and logs, LogMap outputs and evaluation harness, and LLM benchmark are released under CC-BY-4.0.The repository is https://github.com/fabio-rovai/ies-hqdm-crosswalk.Source: A. Data and code availability · p. 13
• All materials reproduce with python reasoning/orientation_search.py given any JDK; input ontologies are public under their stated licenses, and the work is independent and unaffiliated with the named organizations.The passage lists IES under OGL v3, HQDM under Apache-2.0 and Crown Copyright, and BFO 2020 under CC-BY; it says the work is not affiliated with or endorsed by Dstl, GCHQ, the IES Working Group, or the NDTP.Source: A. Data and code availability · p. 13