Foundational Research: Ontology-Native AI
Beyond existence: certified denotation
The closed-world vocabulary gate guarantees one thing: every term a model emits exists in the ontology. That is necessary, and it is not sufficient. A model can use only real terms and still be wrong, by putting a real property on the wrong kind of thing. Catching that is the next gate, and it is harder. This is a roadmap, stated as one: what certified denotation is, why it is more than the existence check, and how far the honest work has and has not gone.
The error the existence gate cannot see
Consider a graph that types a document as a schema:Person and gives it a schema:birthDate. Every term is real; every term is declared. The vocabulary gate passes it, correctly, because nothing is fabricated. And yet the assertion is nonsense: a document does not have a birth date. The model used the right symbols in an unsound arrangement. Existence checking is blind to this by design, because existence is a property of each term in isolation, and the error is in the relationship between them. The failure has moved up a level, from "is this term real?" to "does this term denote something that can stand in this relation?".
The first rung: domain and range
The ontology already carries part of the answer. Most well-built vocabularies declare, for each property, the classes its subject and object are expected to belong to, its domain and range. schema:birthDate has a domain that does not include documents. So the first rung of certified denotation is a reasoning check: materialise the types implied by the properties used, and test them against what the data asserts, flagging the contradictions. This is standard description-logic territory, and our open-ontologies engine already exposes the reasoning and structural-conformance primitives it needs. It is more expensive than the vocabulary gate and it is not free of judgement, because open-world ontologies often under-specify domain and range on purpose, but it catches a large, important class of right-symbol-wrong-place errors the existence gate waves through.
The hard rung: a certified world model
Domain and range catch type errors. They do not catch a graph that is type-correct but describes a state of affairs that cannot hold: an event whose end precedes its start, a part-whole loop, a participation with no participant. Certifying against that requires more than the ontology's declarations; it requires a model of which world states the ontology can consistently represent, and a check that the generated graph denotes one of them. This is the direction of our 4D grounding work and the broader programme of compiling ontologies into certified world models. It is genuinely open research. We are not claiming a solved gate here, and it would be dishonest to. What we are claiming is the shape of the ladder: existence, then type soundness, then world-state soundness, each a stricter and more expensive guarantee than the last.
"Proving a term exists is the floor, not the ceiling. Above it sits type soundness, and above that, whether the graph describes a world the ontology can actually hold. Each rung costs more and buys more. The mistake is stopping at the floor and calling it correctness."
Fabio Rovai, Tesseract Academy
The floor is built and measured: see the vocabulary-gate benchmark and run it yourself below. The upper rungs are where the work goes next, and we will report them the same way, with the weak spots named.
Start at the floor
The existence gate, live in your browser or in Colab, with the full benchmark on GitHub.
