Stability in Abstract Argumentation

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 argumentbased negotiation.

Stability and Relevance in Incomplete Argumentation Frameworks

“…Specifically, first we (re)define stability on IAFs, considering not only IN, but also OUT and UNDEC justification statuses. This results in a more finegrained notion of stability than an earlier definition in [6]. Second, we present precise complexity results for stability of all these justification statuses in grounded, complete, stable and preferred semantics, refining preliminary results in [6].…”

“…This results in a more finegrained notion of stability than an earlier definition in [6]. Second, we present precise complexity results for stability of all these justification statuses in grounded, complete, stable and preferred semantics, refining preliminary results in [6]. Third, we define a notion of relevance in the context of reaching stability in IAFs.…”

“…However, in practice, argumentation is a dynamic process in which not all arguments may be known in advance. Incomplete argumentation frameworks (IAFs) are designed to handle this dynamic process by extending AFs to allow for both certain and uncertain arguments and attacks [3,4,5,6]. In this paper, we study two problems in IAFs and their complexity for various semantics: stability and relevance.…”

“…Detecting stability was initially introduced for the ASPIC + framework in [7] and subsequently studied for structured and abstract argumentation settings in [8,6]. Informally, an argument is stable if more information cannot change its justification status.…”

“…Stability detection has practical applications, for instance as a termination criterion for argumentative dialogue agents: in the agent architecture for inquiry proposed in [8], stability detection prevents the agent from asking unnecessary questions. In addition, [6] proposes an application of stability detection in negotiating agents, to recognise situations in which an agent should stop negotiating and accept its opponent's offer.…”