Reasoning in Rough Description Logics with Multiple Indiscernibility Relations

Rough description logics (DLs) can express approximations of concepts by partitioning the interpretation domain into so-called granules by an indiscernibility relation. Admitting a family of indiscernibility relations yields multi-granular partitionings which can interact with each other. In this paper, we investigate reasoning in rough DLs with multiple indiscernibility relations. We focus on the extension of rough EL with linear multigranulation orders, where granulations are structured from finest to coarsest, and provide a polynomial-time procedure for deciding concept subsumption. If the indiscernibility relations are not linearly ordered, subsumption becomes ExpTime-hard. We also study reasoning in the rough DL SHI(Self) w.r.t. arbitrary multi-granular partitionings, and show that the complexity of reasoning remains exponential, just as in classical ALC.