Extending Forgetting-Based Abduction Using Nominals

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 \(\mathcal {ALC}\) and the observation can contain any set of \(\mathcal {ALC}\) 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 \(\mathcal {ALC}\) which uses nominals, role inverses and fixpoints: \(\mathcal {ALCOI}\mu (\nabla )\). 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.