  Given a knowledge base and an observation as a set of facts, ABox abduction
aims at computing a hypothesis that, when added to the knowledge base, is
sufficient to entail the observation. In signature-based ABox abduction, the
hypothesis is further required to use only names from a given set. This form of
abduction has applications such as diagnosis, KB repair, or explaining missing
entailments. It is possible that hypotheses for a given observation only exist
if we admit the use of fresh individuals and/or complex concepts built from the
given signature, something most approaches for ABox abduction so far do not
support or only support with restrictions. In this paper, we investigate the
computational complexity of this form of abduction -- allowing either fresh
individuals, complex concepts, or both -- for various description logics, and
give size bounds on the hypotheses if they exist.
