Nonmonotonic extensions of low-complexity DLs: complexity results and proof methods

In this paper we propose nonmonotonic extensions of low complexity Description Logics EL and DL-Litecore for reasoning about typicality and defeasible properties. The resulting logics are called EL⊥Tmin and DL-LitecTmin. We summarize complexity results for such extensions recently studied. Entailment in DL-LitecTmin is in Π p 2 , whereas entailment in EL ⊥ Tmin is EXPTIMEhard. However, considering the known fragment of Left Local EL⊥Tmin, we have that the complexity of entailment drops to Π 2 . Furthermore, we present tableau calculi for EL⊥Tmin (focusing on Left Local knowledge bases) and DL-LitecTmin. The calculi perform a two-phase computation in order to check whether a query is minimally entailed from the initial knowledge base. The calculi are sound, complete and terminating. Furthermore, they represent decision procedures for Left Local EL⊥Tmin knowledge bases and DL-LitecTmin knowledge bases, whose complexities match the above mentioned results.