We extend the description logic EL++ with reflexive roles
and range restrictions, and show that subsumption remains tractable if
a certain syntactic restriction is adopted. We also show that subsumption
becomes PSpace-hard (resp. undecidable) if this restriction is weakened
(resp. dropped). Additionally, we prove that tractability is lost when
symmetric roles are added: in this case, subsumption becomes ExpTime-
hard
R. Straeten, T. Mens, J. Simmonds, and V. Jonckers. UML 2003 – The Unified Modeling Language, volume 2863 of Lecture Notes in Computer Science, page 326--340. Springer, (2003)
D. Frankel, P. Hayes, E. Kendall, and D. McGuinness. 1st International Workshop on the Model-Driven Semantic Web (MDSW2004), Monterey, California, USA, (September 2004)