Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocabulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present the first complete method solving signature-based abduction for observations expressed in the expressive description logic ALC, which can include TBox and ABox axioms, thereby solving the knowledge base abduction problem. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.

Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC) ontologies. Non-abducibles are specified by a forgetting signature which can contain concept, but not role, symbols. The resulting hypotheses are semantically minimal and each consist of a set of disjuncts. These disjuncts are each independent explanations, and are not redundant with respect to the background ontology or the other disjuncts, representing a form of hypothesis space. The observations and hypotheses handled by the method can contain both atomic or complex ALC concepts, excluding role assertions, and are not restricted to Horn clauses. Two approaches to redundancy elimination are explored for practical use: full and approximate. Using a prototype implementation, experiments were performed over a corpus of real world ontologies to investigate the practicality of both approaches across several settings.

Uniform interpolation and the dual task of forgetting restrict the ontology to a specified subset of concept and role names. This makes them useful tools for ontology analysis, ontology evolution and information hiding. Most previous research focused on uniform interpolation of TBoxes. However, especially for applications in privacy and information hiding, it is essential that uniform interpolation methods can deal with ABoxes as well. We present the first method that can compute uniform interpolants of any ALC ontology with ABoxes. ABoxes bring their own challenges when computing uniform interpolants, possibly requiring disjunctive statements or nominals in the resulting ABox. Our method can compute representations of uniform interpolants in ALCO. An evaluation on realistic ontologies shows that these uniform interpolants can be practically computed, and can often even be presented in pure ALC.