Relations between Ontologies

In the previous section, we have shown operations that relate ontologies. A classification of the degree of translatability between two ontologies is provided in FIPA Ontology Service Specification:

Extension - ontology O₁ extends ontology O₂. The ontology O₁ extends or includes the ontology O₂. Informally this means that all the symbols that are defined within the O₂ are found in the O₁ together with the restrictions, meanings and other axiomatic relations of these symbols from O₂.
Identical - ontologies O₁ and O₂ are identical. Vocabulary, axiomatization and the language are physically identical, but the name can be different.
Equivalent - ontologies O₁ and O₂ are equivalent. Logical vocabulary and logical axiomatization are the same, but the language (syntax) is different. When O₁ and O₂ are equivalent then they are strongly translatable in both ways.
Strongly-translatable - source ontology O₁ is strongly translatable to the target ontology O₂. The vocabulary of O₁ can be totally translated to the vocabulary of O₂, axiomatization from O₁ holds in O₂, there is no loss of information from O₁ to O₂ and there is no introduction of inconsistency. Note that the representation languages can still be different.
Weakly-translatable - source ontology O₁ is weakly translatable to the target ontology O₂. The translation permits some loss of information (e.g. the terms are simplified in O₂), but doesn't permit introduction of inconsistency.
Approx-translatable - source ontology O₁ is approximately translatable to the target ontology O₂. The translation permits even introduction of inconsistencies, i.e. some of the relations become no more valid and some constraints do not apply anymore.

Like with the operations in the previous section, deciding the relationship between two ontologies often requires manual intervention. Also, one is usually interested also in the way of translating between translatable ontologies. Once the relationship is known, it can be used for deciding what ontologies to select for particular purposes.