  The question whether an ontology can safely be replaced by another, possibly
simpler, one is fundamental for many ontology engineering and maintenance
tasks. It underpins, for example, ontology versioning, ontology modularization,
forgetting, and knowledge exchange. What safe replacement means depends on the
intended application of the ontology. If, for example, it is used to query
data, then the answers to any relevant ontology-mediated query should be the
same over any relevant data set; if, in contrast, the ontology is used for
conceptual reasoning, then the entailed subsumptions between concept
expressions should coincide. This gives rise to different notions of ontology
inseparability such as query inseparability and concept inseparability, which
generalize corresponding notions of conservative extensions. We survey results
on various notions of inseparability in the context of description logic
ontologies, discussing their applications, useful model-theoretic
characterizations, algorithms for determining whether two ontologies are
inseparable (and, sometimes, for computing the difference between them if they
are not), and the computational complexity of this problem.
