A conceptual incompatibility between controlled vocabularies, taxonomies or formal ontologies—arising from differences in granularity, scope, definition, modeling choices or underlying worldview—that prevents reliable one‑to‑one semantic alignment or causes lossy or ambiguous mappings.

Principle

Conceptual models encode modelling choices (classes, properties, scope) that determine entailments; when two ontologies make different modelling commitments, naïve mappings produce incorrect inferences, ambiguity or information loss because equivalent labels do not guarantee equivalent semantics.

Demonstration

Situation: Two domain ontologies represent the notion of 'event' with different subclass structures and different temporal properties. Recognition: An integrator attempts automatic alignment by label matching. Action: The integrator applies a one‑to‑one mapping and runs a reasoner. Consequence: The reasoner derives contradictory assertions for some instances and drops relationships that cannot be reconciled, producing misleading query results and erroneous aggregation.

Misapplication

Assuming lexical equivalence implies semantic equivalence. The error is to map concepts solely by label or superficial metadata without examining scope, definitions and axioms; such mappings obscure deeper modelling differences and propagate incorrect assertions.

Consequence

Faulty query results, invalidated inferences, loss of detail during integration, and brittle federated services; these follow because downstream reasoning and joins depend on the semantic commitments encoded in each ontology.

Reversal

When explicit mapping ontologies, mediation layers, or alignment axioms (including many‑to‑many, skos:related, or context‑conditioned mappings) are created and their provenance recorded, mismatch is manageable: partial or contextual mappings can preserve meaning without forcing incorrect equivalence.

Boundary

Clearly within: Two controlled vocabularies use the same label for concepts that have different scopes and hierarchical relations. Boundary case: Concepts overlap partially and require many‑to‑many mappings with conditional rules. Clearly outside: Purely syntactic differences (different serialisations of the same OWL ontology) where the underlying model and axioms are identical.

Semantic Tension

Expressivity ↔ Interoperability — richer, more expressive ontologies capture domain nuance but reduce the likelihood of simple, lossless alignment across independently developed models.

Synthesis

Ontology mismatch is not merely a naming problem but a modelling one: reliable integration requires explicit alignment artifacts, provenance, and acceptance that many mappings will be partial, context‑dependent or lossy; governance and mediation reduce risk but cannot eliminate the need for interpretive decisions.