TBox abduction explains why an observation is not entailed by a TBox, by computing multiple sets of axioms, called explanations , such that each explanation does not entail the observation alone while appending an explanation to the TBox renders the observation entailed but does not introduce incoherence. Considering that practical explanations in TBox abduction are likely to mimic minimal explanations for TBox entailments, we introduce admissible explanations which are subsets of those justifications for the observation that are instantiated from a finite set of justification patterns. A justification pattern is obtained from a minimal set of axioms responsible for a certain atomic concept inclusion by replacing all concept (resp. role) names with concept (resp. role) variables. The number of admissible explanations is finite but can still be so large that computing all admissible explanations is impractical. Thus, we introduce a variant of subset-minimality, written ⊆ ds -minimality, which prefers fresh (concept or role) names than existing names. We propose efficient methods for computing all admissible ⊆ ds -minimal explanations and for computing all justification patterns, respectively. Experimental results demonstrate that combining the proposed methods is able to achieve a practical approach to TBox abduction.

ABox abduction plays an important role in reasoning over description logic (DL) ontologies. However, it does not work with inconsistent DL ontologies. To tackle this problem while achieving tractability, we generalize ABox abduction from the classical semantics to an inconsistency-tolerant semantics, namely the Intersection ABox Repair (IAR) semantics, and propose the notion of IAR-explanations in inconsistent DL ontologies. We show that computing all minimal IAR-explanations is tractable in data complexity for first-order rewritable ontologies. However, the computational method may still not be practical due to a possibly large number of minimal IAR-explanations. Hence we propose to use preference information to reduce the number of explanations to be computed.

ABox abduction is an important reasoning mechanism for description logic ontologies. It computes all minimal explanations (sets of ABox assertions) whose appending to a consistent ontology enforces the entailment of an observation while keeps the ontology consistent. We focus on practical computation for a general problem of ABox abduction, called the query abduction problem, where an observation is a Boolean conjunctive query and the explanations may contain fresh individuals neither in the ontology nor in the observation. However, in this problem there can be infinitely many minimal explanations. Hence we first identify a class of TBoxes called first-order rewritable TBoxes. It guarantees the existence of finitely many minimal explanations and is sufficient for many ontology applications. To reduce the number of explanations that need to be computed, we introduce a special kind of minimal explanations called representative explanations from which all minimal explanations can be retrieved. We develop a tractable method (in data complexity) for computing all representative explanations in a consistent ontology. xperimental results demonstrate that the method is efficient and scalable for ontologies with large ABoxes.

ABox abduction is an important aspect for abductive reasoning in Description Logics (DLs). It finds all minimal sets of ABox axioms that should be added to a background ontology to enforce entailment of a specified set of ABox axioms. As far as we know, by now there is only one ABox abduction method in expressive DLs computing abductive solutions with certain minimality. However, the method targets an ABox abduction problem that may have infinitely many abductive solutions and may not output an abductive solution in finite time. Hence, in this paper we propose a new ABox abduction problem which has only finitely many abductive solutions and also propose a novel method to solve it. The method reduces the original problem to an abduction problem in logic programming and solves it with Prolog engines. Experimental results show that the method is able to compute abductive solutions in benchmark OWL DL ontologies with large ABoxes.