Reasoning About Typicality in Low Complexity DLs: the Logics EL⊥Tmin and DL-LitecTmin

We propose a nonmonotonic extension of low complexity Description Logics EL⊥ and DL-Litecore for reasoning about typicality and defeasible properties. The resulting logics are called EL⊥ T min and DL-Litec T min . Concerning DL-Litec T min , we prove that entailment is in \Pi^p_2. With regard to EL⊥ T min , we first show that entailment remains EXPTIME-hard. Next we consider the known fragment of Left Local EL⊥ T min and we prove that the complexity of entailment drops to \Pi^p_2.