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 \(\mathcal {E\!L}\) 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 \(\textsc {ExpTime}\) -hard. We also study reasoning in the rough DL \(\mathcal {SHI}(\textsf{Self}) \) w.r.t. arbitrary multi-granular partitionings, and show that the complexity of reasoning remains exponential, just as in classical \(\mathcal {ALC}\) .