Reasoning about typicality in low complexity DLs: the logics EL^bot T_min and DL-lite_R T_min
Laura Giordano, Valentina Gliozzi, Nicola Olivetti and Gian Luca Pozzato
In this paper, we propose a non-monotonic extension of low complexity Description Logics EL^\bot and DL-lite_R for reasoning about typicality and defeasible properties. The resulting logics are called EL^\bot T_min and DL-lite_R T_min. Concerning DL-lite_R T_min, we prove that entailment is in \Pi^p_2. With regard to EL^\bot T_min, we first show that entailment remains ExpTime-hard. Next we consider the known fragment of Left Local EL^\bot T_min and we prove that the complexity of entailment drops to \Pi^p_2.