Anselm Haak

Anselm Haak, Patrick Koopmann, Yasir Mahmood et al.

Given a knowledge base (KB) with a non-entailed fact, the ABox abduction problem asks for possible extensions of the KB that would entail this fact. This problem has many applications, ranging from diagnosis to explainability and repair. ABox abduction has been well-investigated for consistent KBs and classical semantics, but little is known for the case of inconsistent KBs, which can be caused by erroneous data. In this paper we define suitable notions of abduction in this setting and propose criteria that guide abduction towards "useful" hypotheses. To regain meaningful reasoning in the presence of inconsistencies, we use well-established repair semantics. We provide a comprehensive landscape of the complexity of ABox abduction under repair semantics, treating different variants of the abduction problem for the light-weight description logics DL-Lite and EL_bot.

Anselm Haak, Patrick Koopmann, Yasir Mahmood et al.

Abduction is a central approach to explain missing entailments from a knowledge base by providing a hypothesis, that would, if added to the knowledge base, make the missing entailment become true. Abduction under repair semantics has recently been investigated in detail, where several desirable properties and optimality criteria were considered, such as signature-restrictions and minimality in size and of introduced conflicts. Naturally, hypotheses that satisfy more than one of these properties or combine a property with an optimality criterion would be even more desirable for applications. So far, such hypotheses have not been investigated in the literature. In the present paper, we consider the ABox abduction problem for hypotheses satisfying more than one property or additional optimality criteria, for EL_bot under brave and AR semantics. Our main observation is that often requiring additional properties for hypotheses does not lead to an increase of complexity.