An argumentation system for reasoning with conflict-minimal paraconsistent ALC

TL;DR

This paper introduces an argumentation framework for reasoning with conflict-minimal paraconsistent ALC, addressing non-monotonicity in semantic interpretations to improve reasoning in inconsistent knowledge bases.

Contribution

It proposes an assumption-based argumentation system that captures conflict-minimal interpretations in paraconsistent ALC, handling non-monotonic reasoning effectively.

Findings

The system supports reasoning with conflict-minimal interpretations.

It ensures conclusions are supported across all stable extensions.

Addresses non-monotonicity in paraconsistent logic reasoning.

Abstract

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.