An axiomatic analysis of structured argumentation for prioritized default reasoning

Several systems of argument-based and non-argument-based semantics have been proposed for prioritized default reasoning. As the proposed semantics often sanction contradictory conclusions (even for skeptical reasoners), there is a fundamental need for guidelines for understanding and evaluating them, especially their conceptual foundations and relationships. In this paper, we introduce several natural axioms for structural argumentation with preferences that capture both the consistency and closure postulates. We show that Aspic+ semantics do not satisfy key axioms including the consistency postulate and propose a simple one satisfying all axioms. We show that the prescriptive non-argument-based approach to prioritized default reasoning is sound (and complete for a relevant class of knowledge bases) wrt our proposed simple semantics.