We investigate how multiple ranking-based semantics can be aggregated into a single ranking-based semantics for abstract argumentation frameworks. For that, we phrase this problem as a judgment aggregation problem and utilise ideas from voting theory for aggregating preorders. We show, that in our approach, the relationship between two arguments is preserved in cases where all ranking-based semantics agree on the relationship. We analyse the resulting ranking-based semantics axiomatically and demonstrate that the satisfaction of the principles can be transferred to the aggregated setting when all, or at least a majority, of the ranking-based semantics satisfy the principles.
This paper studies argumentation protocols in abstract argumentation. Existing approaches rely on framework-specific definitions, which make comparisons between protocols difficult. We propose a unified framework that distinguishes three components: protocol rules, contextual parameters, and a debate function capturing the evolution of a debate. We define a set of principles on this function to analyze protocol behavior. Our framework can represent argumentation protocols from the literature, and supports the analysis and comparison of their executions.
In this paper we present a formal Toulmin Argumentation Logic (TAL) based on Toulmin’s original argument scheme, and establish a formal correspondence between TAL and the ASPIC+ framework for structured argumentation. Thus, we provide Toulmin’s account with a precise notion of argument acceptability grounded in Dung’s theory of abstract argumentation frameworks. Furthermore, the formalisation has direct practical relevance for recent work that uses Toulmin’s scheme in the context of large language models.
What makes an argument genuinely acceptable? Can acceptance be grounded in self-assertion alone, or does it require third-party, external corroboration — and if so, what formal notion of admissibility captures this requirement without collapsing into triviality? We show that this problem can be analysed from the perspective of symmetric argumentation frameworks, where Dung’s admissibility and strong admissibility fail to provide meaningful discrimination. We introduce external admissibility as a middle notion between them. It requires every accepted argument to be defended by a third party, ruling out circular self-assertion while preserving mutual corroboration. This notion occupies a strict intermediate position in the admissibility hierarchy, and the structural conditions under which all three notions coincide can be identified through the reduced framework.
