[Paper Review] Stability in Abstract Argumentation

Jean-Guy Mailly, Julien Rossit|arXiv (Cornell University)|Dec 23, 2020

Multi-Agent Systems and Negotiation24 references4 citations

TL;DR

This paper introduces and formalizes the notion of stability in abstract argumentation frameworks (AFs), showing that checking whether an argument's acceptability status is immune to future changes is equivalent to reasoning with Argument-Incomplete AFs (IAFs). The authors establish complexity bounds for stability under four prominent semantics (grounded, stable, preferred, complete) and demonstrate its utility in automated negotiation, where agents can strategically shift offers once stability is confirmed.

ABSTRACT

The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away from the logical structure of arguments, and we transpose this notion of stability to the context of Dungean argumentation frameworks. In particular, we show how this problem can be translated into reasoning with Argument-Incomplete AFs. Then we provide preliminary complexity results for stability under four prominent semantics, in the case of both credulous and skeptical reasoning. Finally, we illustrate to what extent this notion can be useful with an application to argument-based negotiation.

Motivation & Objective

• To adapt the concept of stability—originally defined in structured argumentation—to abstract argumentation frameworks (AFs).
• To formalize stability as a property ensuring an argument's acceptability status remains unchanged under any future evolution of the AF.
• To reduce the problem of stability checking to well-known reasoning tasks in Incomplete Argumentation Frameworks (IAFs).
• To analyze the computational complexity of stability under four major semantics: grounded, stable, preferred, and complete.
• To demonstrate the practical relevance of stability in automated negotiation, where agents can make strategic decisions once stability is confirmed.

Proposed method

• The paper defines stability in abstract AFs as a property where an argument’s acceptability status is invariant under any future modification of the framework.
• It establishes a formal reduction of stability checking to reasoning tasks in Incomplete AFs (IAFs), where some attacks may be uncertain or unknown.
• The authors use extension-based semantics (grounded, stable, preferred, complete) to define acceptability and analyze stability under each.
• Complexity results are derived by relating stability to credulous and skeptical reasoning in IAFs, leveraging known complexity classes.
• An application scenario in automated negotiation is presented, illustrating how stability enables agents to switch offers strategically once stability is verified.
• Theoretical analysis includes both upper and lower bounds for the complexity of stability checking under each semantics.

Experimental results

Research questions

• RQ1 How can the notion of stability from structured argumentation be formally adapted to abstract argumentation frameworks?
• RQ2 What is the computational complexity of checking stability under the grounded, stable, preferred, and complete semantics in abstract AFs?
• RQ3 Can stability checking be reduced to known reasoning tasks in Incomplete Argumentation Frameworks (IAFs)?
• RQ4 How can stability be leveraged in practical scenarios such as automated negotiation?
• RQ5 What are the implications of stability for reasoning under uncertainty in argumentation frameworks?

Key findings

• Stability in abstract AFs is formally defined as the invariance of an argument’s acceptability status under any future evolution of the framework.
• The problem of checking stability is reducible to reasoning tasks in Incomplete AFs, enabling the use of existing IAF-solving techniques.
• The paper provides complexity bounds for stability under all four major semantics: grounded, stable, preferred, and complete, with both credulous and skeptical reasoning variants.
• For all four semantics, the complexity of stability checking is shown to be within known complexity classes, with precise upper and lower bounds established.
• The application to automated negotiation demonstrates that stability allows agents to make strategic, forward-looking decisions—such as switching to a second-best offer—once stability is confirmed.
• The work opens new research directions, including extending stability to 3-valued labellings, preference-based AFs, and frameworks with uncertain attack relations.