Deciding the logical difference problem for EL with role inclusions

We consider the logical difference problem for terminologies that are formulated in the lightweight description logic EL with role inclusions for role hierarchies, transitivity, and right-identity. The main result is that deciding whether two terminologies are logically different wrt. a signature can be done in ExpTime, thus it is more difficult than the subsumption problem for this logic but not more difficult than deciding logical difference without role inclusions. This paper extends the result for EL by Lutz and Wolter [11].