Are inferences in OWL made for use only in the construction and maintenance of an ontology, or can they also be useful in the system in which the ontology is inserted? If it is the second case, could you give an example? I don't know so many systems using ontologies, then I expect a clarification about the role of inferences in ontologies and ontology-based systems.
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Inferences are used extensively in the bioinformatics community where ontologies are used to infer classification hierarchies in the annotation of biological data. See for example the Ontology Lookup Service (OLS) (Disclaimer: I am a maintainer of OLS).
As an example, look at liver disease. On the righthand side you will see some of the axioms used in its definition. These are axioms used in inferring the hierarchical structure of the ontology and the placement of liver disease in the hierarchy :
How is this useful? When a user sees that some data is annotated with EFO_0001421 (liver disease) they can get additional context information from the ontology. I.e., that liver disease is considered to be a digestive system disease and an endocrine system disease. Moreover, by looking at the children of liver disease, they can find all the diseases that are considered to be liver diseases.