Repairing missing is-a structure in ontologies is an abductive reasoning problem

With the increased use of ontologies in semantically-enabled applications, the issue of debugging defects in ontologies has become increasingly important. These defects can lead to wrong or incomplete results for the applications. Debugging consists of the phases of detection and repairing. In this paper we focus on the repairing phase of a particular kind of defects, i.e., the missing relations in the is-a hierarchy. We show that this can be formalized as an abduction problem. Further, we define properties for the ontology, the set of is-a relations to repair and the domain expert, as well as preference criteria on solutions and discuss the influences of these properties and criteria on the existence of solutions for the abduction problem. We also discuss the consequences of our analyses of the repairing problem for the development and use of debugging systems