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.

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 vocab- ulary 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. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.

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Abductive reasoning produces hypotheses to explain new observations with respect to some background knowledge. This paper focuses on ABox abduction in ontologies, where knowledge is expressed in description logics and both the observations and hypotheses are ground statements. The input is expressed in the description logic ALC and the observation can contain any set of ALC concept or role assertions. The proposed approach uses forgetting to produce hypotheses in the form of a disjunctive set of axioms, where each disjunct is an independent explanation for the observation and the overall hypothesis is semantically minimal, i.e., makes the least assumptions required. Previous work on forgetting-based abduction is combined with the semantic forgetting method of the system FAME. The hypotheses produced are expressed in an extension of ALC which uses nominals, role inverses and fixpoints: ALCOIµ(∇). This combination overcomes the inability of the existing forgetting-based approach to allow role assertions in observations and hypotheses, and enables the computation of other previously unreachable hypotheses. An experimental evaluation is performed using a prototype implementation of the method on a corpus of real world ontologies.

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