An argumentation system for reasoning with conflict-minimal paraconsistent ALC
This addresses inconsistency issues in the semantic web for AI and knowledge representation, but it is incremental as it builds on existing paraconsistent logic and argumentation frameworks.
The paper tackles the problem of reasoning with inconsistent knowledge in the semantic web by proposing an argumentation system based on conflict-minimal paraconsistent ALC, which ensures that conclusions align with standard semantics when knowledge is consistent while handling non-monotonicity through stable extensions.
The semantic web is an open and distributed environment in which it is hard to guarantee consistency of knowledge and information. Under the standard two-valued semantics everything is entailed if knowledge and information is inconsistent. The semantics of the paraconsistent logic LP offers a solution. However, if the available knowledge and information is consistent, the set of conclusions entailed under the three-valued semantics of the paraconsistent logic LP is smaller than the set of conclusions entailed under the two-valued semantics. Preferring conflict-minimal three-valued interpretations eliminates this difference. Preferring conflict-minimal interpretations introduces non-monotonicity. To handle the non-monotonicity, this paper proposes an assumption-based argumentation system. Assumptions needed to close branches of a semantic tableaux form the arguments. Stable extensions of the set of derived arguments correspond to conflict minimal interpretations and conclusions entailed by all conflict-minimal interpretations are supported by arguments in all stable extensions.