Decidability of Circumscribed Description Logics Revisited.

We revisit non-monotonic description logics based on circumscription with preferences and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property DL-Lite $_{\mathcal{F}}$ and $\mathcal{ALCFI}$ and with fixed roles DL-Lite $_{\mathcal{F}}$ and a fragment of DL-Lite $_{\mathcal{R}}$ , improving upon previous decidability results that are limited to logics which have the finite model property and do not allow to fix roles during minimization.