An illustration of semantic inference running on the mapping directed from node a to b. Given two ontologies O1 and O2, the sentence "a mapping-to b" (a ∈ O1, b ∈ O2) can be inferred by a reasoning engine. For any child node ai of a, we can infer that "ai maps-to b". Similarly, for any parent node bj of b, we can infer that "a mapping-to bj". Furthermore, for any child node ai of a, any parent node bj of b, the assertions of "ai mapping-to bj" are also valid.