cs.MA · 2605.23578 Copy arXiv ID · May 22, 2026 Save Safety, Liveness, and Fairness in Quantitative Argumentation Dialogues Authors: Arunavo Ganguly , Julian Alfredo Mendez , Timotheus Kampik
Organizations: Department of Computing Science, Umeå University, Umeå, Sweden.
Abstract We introduce notions of safety, liveness, and fairness, as commonly used in temporal reasoning, to quantitative (bipolar) argumentation dialogues where repeated inferences are drawn from argumentation graphs with weighted nodes. Between inferences, these graphs undergo updates. Strong and weak safety capture that arguments' (final) strengths remain above a specific threshold of justification and always reach the threshold eventually, respectively. Liveness requires that arguments' strengths fluctuate across the threshold of justification. Fairness notions assess how safe arguments are spread within a sequence of argumentation graphs. We formally show how these notions are related, and discuss some analytical challenges with respect to providing general guarantees for our properties.
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May 3, 2026 · cs.AI J/K move · Enter open · S save
Uri Andrews, Luca San Mauro, John Spoerl
Department of Mathematics, University of Wisconsin–Madison · Dipartimento di Ricerca e Innovazione Umanistica, University of Bari, Italy
In Dung-style abstract argumentation, various semantics capture notions of acceptability of arguments. The admissibility semantics capture the notion that an argument can be consistently defended from any potential counterargument. Weak semantics often relax the demands of admissibility by restricting which counterarguments must be taken seriously (e.g., discounting self-defeating or otherwise incoherent attacks). Many prominent proposals for weak semantics remain extension-based in a stronger sense. While these semantics discount attacks from arguments which are considered unreasonable, they still require a uniform defense against all reasonable arguments, even if they are collectively inconsistent. This uniformity can be too demanding when defensibility is inherently strategic, and thus the appropriate reply depends on the opponent's line of attack. We introduce tenability, a family of dialogue-based semantics that formalize when a designated argument (or a set of arguments) can be maintained in debate by a proponent against any conflict-free attack which the opponent may present. The approach is motivated by three natural benchmark patterns: self-defeating attack, floating assignment, and disjunctive reinstatement, on which tenability behaves differently from all weak semantics previously considered in the literature. We define three variants -- static tenability, tenability, and strong tenability -- via monotone commitment games over finite conflict-free moves, differing in the obligations imposed on the disputants. We establish the relative strength of these notions, prove implications and separations with previously studied weak semantics, and we analyze computational complexity on finite frameworks: deciding static tenability is
Π 2 P Π^P_2 Π 2 P -complete, while deciding tenability and strong tenability is PSPACE-complete.