Defeasible Inclusions in Low-Complexity DLs: Preliminary Notes

We analyze the complexity of reasoning with circumscribed low-complexity DLs such as DL-lite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DL-lite_R complexity drops from NExp^NP to the second level of the polynomial hierarchy. In EL, reasoning remains ExpTime-hard, in general. However, by restricting the possible occurrences of existential restrictions, we obtain membership in Sigma^p₂ and Pi^p₂ for an extension of EL.

Piero A. Bonatti, Marco Faella, Luigi Sauro