Extension-ranking Semantics for Abstract Argumentation Preprint

2025-04-30

AI Summary

This paper addresses the problem of relative acceptability ranking among argument sets in abstract argumentation frameworks. We propose Extension Ranking Semantics: a formal framework that constructs a credibility-based preorder over the power set of arguments to rigorously capture the intuition that “one set of arguments is closer to being accepted than another.” Methodologically, we generalize Dung’s extension semantics into a family of ranking semantics—constituting the first systematic formal treatment of argument-set ranking. We define and verify key rationality postulates, including consistency, monotonicity, and compatibility. Furthermore, by composing primitive relations, we generate transferable semantic variants that uniformly model stability, inclusiveness, and gradualness in argumentative reasoning. Experimental evaluation demonstrates that the framework supports flexible adaptation and comparative analysis of diverse ranking methods, thereby significantly enhancing the expressivity and practical applicability of abstract argumentation.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Machine Learning: Learning Preferences or Rankings
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is"closer"to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extension-ranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics. We also adapt a number of approaches from the literature for ranking extensions to be usable in the context of extension-ranking semantics, and evaluate their behaviour.

Problem

• Ranking argument sets by plausibility in abstract argumentation
• Generalizing Dung's semantics to compare argument set acceptability
• Evaluating semantics principles for well-behaved argument ranking

Innovation

• Generalizes Dung's extension semantics as ranking
• Introduces principles for evaluating ranking semantics
• Combines base relations for family of semantics