Restricted Role-value-maps in a Description Logic with Existential Restrictions and Terminological Cycles

In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic EL, which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics. In this paper we show that subsumption in EL (with or without cyclic definitions) remains polynomial even if one adds a certain restricted form of global role-value-maps to EL. In particular, this kind of role-value-maps can express transitivity of roles.