On the Complexity of the Discussion-based Semantics in Abstraction Argumentation

2026-04-13

AI Summary

This study addresses the computational complexity of comparing argument strength under discussion-based semantics in abstract argumentation. By reformulating the problem as an equivalence-checking task for path-counting between vertices in directed graphs, the work introduces— for the first time—the use of semiring automaton equivalence techniques into abstract argumentation frameworks. Leveraging tools from automata theory and graph theory, the authors develop an efficient decision algorithm that resolves a long-standing open question regarding the complexity of this semantic comparison. The proposed approach not only offers a novel perspective for analyzing the computational properties of argument ranking semantics but also establishes that the equivalence problem is solvable in polynomial time.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Natural Language Processing: Discourse, Pragmatics & Argument Mining
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two vertices in a graph, the number of walks of each length ending in those vertices is the same. We employ results from automata theory and reduce this problem to the equivalence problem for semiring automata. This offers a new perspective on the computational complexity of ranking semantics, an area in which the complexity of many semantics remains open.

Problem

• argumentation semantics
• discussion-based semantics
• computational complexity
• graph walks
• ranking semantics

Innovation

• discussion-based semantics
• computational complexity
• semiring automata
• argumentation frameworks
• polynomial-time decidability