Signature-Based Abduction with Fresh Individuals and Complex Concepts for Description Logics (Extended Version)

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.