Tenability and Weak Semantics: Modeling Non-uniform Defense -- Extended Version

2026-05-03

AI Summary

This work addresses the limitations of traditional weak semantics in abstract argumentation, which enforces a uniform defense against all admissible attacks and thus fails to capture nuanced, path-dependent rebuttals in strategic argumentation. To overcome this, the paper introduces a family of tenability semantics grounded in a monotonic commitment game framework, formalizing dynamic interactions between proponent and opponent through finite, conflict-free move sequences that permit flexible, attack-path-sensitive defense strategies. It defines three novel variants—static, ordinary, and strong tenability—each relaxing the uniform-defense constraint and exhibiting distinctive behaviors in benchmark scenarios such as self-defeating attacks, floating assignments, and disjunctive reinstatement. Theoretical analysis establishes their relative logical strengths, clarifies their relationships to existing weak semantics, and proves that static tenability is Π²ₚ-complete while ordinary and strong tenability are PSPACE-complete.

Abstract

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 $Π^P_2$-complete, while deciding tenability and strong tenability is PSPACE-complete.

Problem

• abstract argumentation
• weak semantics
• non-uniform defense
• tenability
• admissibility

Innovation

• tenability
• dialogue-based semantics
• weak semantics
• argumentation frameworks
• computational complexity