Defaults in Description Logics:
                   So Simple, So Difficult

                                   Piero Bonatti

                Università degli Studi di Napoli “Federico II”, Italy

    Frame systems—the ancestors of Description Logics—supported a form of
defeasible inheritance and overriding. Such nonmonotonic features disappeared
from implementations after the logical reconstruction of frame systems, although
applications provide interesting use cases for nonmonotonic inferences. This talk
gives an overview of the nonmonotonic DLs introduced so far, and illustrates
the many complexity issues that affect them (which probably explain the lack of
support to nonmonotonic reasoning in DL reasoners). Research never surrenders,
though: a pragmatic change of perspective yields encouraging results, that bring
the quest for low-complexity, nonmonotonic DLs closer to its goal.