The proposed approach can be extended to handle inconsistencies in the TBox by integrating a mechanism that allows for the identification and management of TBox axioms that contribute to inconsistency. This can be achieved by employing a dual-layer reasoning framework where both the ABox and TBox are treated probabilistically.
Probabilistic TBox Axioms: Similar to how ABox axioms are associated with probabilities in the DISPONTE semantics, TBox axioms can also be assigned probability values. This would allow the system to express uncertainty regarding the validity of certain TBox axioms, enabling the reasoning process to consider TBox inconsistencies alongside ABox inconsistencies.
Conflict Detection: The approach can incorporate mechanisms to detect conflicts within the TBox. By analyzing the relationships between TBox axioms, the system can identify which axioms are in conflict and assign them a lower probability of being true. This would allow the reasoner to compute a set of consistent TBox axioms that can be used in conjunction with the ABox.
Repair Strategies: The repair strategies can be adapted to include TBox axioms. When a query is made, the system can generate repairs that not only remove conflicting ABox axioms but also consider the removal or modification of TBox axioms that lead to inconsistency. This would involve creating a set of possible repairs that include both ABox and TBox adjustments.
Unified Reasoning Framework: By creating a unified reasoning framework that simultaneously addresses both ABox and TBox inconsistencies, the system can provide a more comprehensive solution for managing knowledge bases. This would involve extending the tableau algorithm to account for TBox axioms and their interactions with ABox assertions.