cs.AIAug 22, 2026
SaveConsistency Is Not Coherence: Orientation Search for Certified Alignments Between 4D Defence Upper Ontologies
Organizations: The Tesseract Academy (Kampakis and Co Ltd), 5 Brunswick Park Gardens, London N11 1EJ, United Kingdom
Abstract
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.
Figures & tables
| Ontology | triples | named classes | object props | disjointness | unsat (alone) |
| IES ( ies-common.ttl ) | 4,039 | 511 | 162 | 0 | 0 |
| HQDM ( hqdm.owl ) | 3,127 | 229 | 74 | 14 | 39 |
| BFO 2020 ( bfo.owl ) | 1,221 | 35 | 0 | 19 | 0 |
Table 1: The three ontologies as measured on the vendored files. Named classes counts rdf:type owl:Class subjects with an IRI. Disjointness counts owl:disjointWith triples; none of the three uses owl:AllDisjointClasses or owl:disjointUnionOf . Unsatisfiable classes are computed by HermiT on each ontology alone.
| Criterion | Result |
| Consistency (a model exists) | passes |
| New unsatisfiable classes (beyond the native 39) | 100 |
| New source-internal subsumptions (S2 violations) | 218 |
Table 2: Naive equivalence promotion of the expert crosswalk. The consistency check, which is what deployment pipelines typically run, passes.
| Source ( ies: ) | Target ( hqdm: ) | Verdict | S2 if reversed |
| Element | spatio_temporal_extent | full | 0 |
| Thing | thing | full | 0 |
| Event | activity | full | 0 |
| PossibleWorld | possible_world | full | 0 |
| ClassOfElement | class_of_spatio_temporal_extent | full | 0 |
| Entity | individual | forward only | 104 |
Table 3: The certified bridge. Prefixes are omitted: every source is ies: and every target hqdm: . The last column is the number of S2 violations the reverse edge would have introduced, which is why the row is one-directional. Every verdict is a reasoner decision, not a curator’s judgement.
| Mapping for ies:Entity | Rest of bridge | IES classes collapsed |
| bfo:material entity | absent | 0 |
| bfo:material entity | absent | 0 |
| bfo:material entity | present | 101 |
| bfo:material entity | present | 100 |
| bfo:history | present | 0 |
Table 4: The cost of one axiom. Every row merges the complete IES and BFO with ies:Element bfo:occurrent , ies:Event bfo:process and ies:State bfo:occurrent held fixed, and varies only how ies:Entity is mapped. Counts are IES classes made unsatisfiable.
| System (pair) | mappings | backbone | false friend | unsat targets | new unsat | S2 viol. |
| LogMap (IES–HQDM) | 24 | 3/1/6 | yes | 2 | 87 | 103 |
| LogMapLt (IES–HQDM) | 36 | 3/1/6 | yes | 2 | 214 | 112 |
| LogMap (IES–BFO) | 2 | 0/1/3 | — | 0 | 0 | 2 |
| certified bridge (IES–HQDM) | 13 | 10/0/0 | no | 0 | 0 | 0 |
Table 5: Matcher outputs on the vendored pairs, evaluated with HermiT under the same criteria as the certified bridge. “Backbone” scores correct target / wrong target / missed against the pair’s gold targets: the ten expert class correspondences for IES–HQDM, the four certified bridge targets for IES–BFO. “Unsat targets” are accepted mappings whose HQDM target is one of the 39 natively unsatisfiable classes. The certified bridge row is the output of § 4.3 .
| System | into HQDM (8) | into BFO (4) | total |
| Qwen3-Coder-30B-A3B-Instruct (8-bit) | 5 | 1 | 6/12 |
| + IES fine-tune | 6 | 1 | 7/12 |
Table 6: Mapping-oracle accuracy against the HermiT-certified bridge. .
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