From Contexts to Values: Context-Dependent Defeat in Abstract Argumentation

Albert Sadowski; Jarosław A. Chudziak

cs.AIAug 16, 2026

From Contexts to Values: Context-Dependent Defeat in Abstract Argumentation

Authors: Albert Sadowski, Jarosław A. Chudziak

Organizations: Faculty of Electronics and Information Technology Warsaw University of Technology Warsaw, Poland

Abstract

In value-based argumentation, an audience's ordering of values decides which attacks succeed as defeats. In many settings the deciding factor is not the audience but the circumstances: the same attack may succeed at one procedural stage, or under one regulation, and fail at another. Context-dependent argumentation frameworks (CDAFs), a model we recently introduced, capture this directly: one attack relation and a defeat function that switches each attack on or off per context, so every context induces an ordinary Dung framework. This raises a reduction question: can one value assignment with per-context orderings reproduce the defeat function, collapsing the CDAF into a VAF? We present a polynomial-time decision procedure for this question and map the harder neighbouring problems, with upper bounds from NP to $Σ^p_3$ . We also present a validated reference implementation and a measurement: representability is rare and falls fast with the number of contexts.

Figures & tables

Panel of Figure 1 — Figure 1: The worked instance. Left: the attack relation $R$ ; the dashed attack $(x,y)$ is the only attack suppressed in some context. Right: the defeat function $\delta$ .

Problem	Semantics	Bound	Status
Cross-context acceptance (all classes)	grounded	in P	closed
Universal acceptance	preferred	$\Pi^{p}_{2}$ -complete	closed
Indefensibility	preferred	coNP-complete	closed
Audience inducibility of $R^{\prime}\subseteq R$	(defeat relation)	$O(n+m)$	closed
VAF-representability	(defeat function)	$O(n^{2}k+nmk)$	closed
Single-context realisability	grounded	in NP	lower bound open

Table 1: Decision problems for a CDAF with

n

arguments,

m

attacks, and

k

contexts. Cross-context bounds follow from single-framework classifications Dvořák and Dunne (2018) with a factor

k

for iterating over contexts; the corresponding audience-dependent questions for VAFs are classified by Bench-Capon et al. (2007) .

	$k=1$	$k=2$	$k=3$	$k=4$
$n=3$	$54.9$	$10.5$	$1.51$	$0.18$
$n=4$	$20.3$	$0.52$	$0.009$	$<0.002$
$n=5$	$4.1$	$0.003$	$<0.002$	$<0.002$

Table 2: Percentage of VAF-representable CDAFs among labeled instances without self-attacks, by arguments

n

and contexts

k

. The cells with

n=3

k\leq 3

are exact (exhaustive enumeration); the others are estimates from

2\times 10^{5}

uniform samples per cell, all 95% confidence intervals below

0.2

percentage points. Cells with no representable sample are bounded above by

0.002

percent.

Computational Argumentation

Computational argumentation studies how to represent, analyze, and apply arguments and their relationships using formal and computational methods.

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Choosing the Lens: Strategic Perspective Activation in Context-Dependent Argumentation

Albert Sadowski, Jarosław A. Chudziak

Warsaw University of Technology

Computational Argumentation

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The same arguments often need to be evaluated under different external regimes. An agent with influence over the regime has a strategic lever that standard formalisms do not directly capture. We introduce context-dependent argumentation frameworks (CDAFs), an extension of Dung's theory in which a defeat function determines, per context, which attacks succeed. A perspective-labeled specialisation derives the defeat function from a relevance set

ρ

and a priority

π

. The relevance set is the agent's action space. In a small worked example, the agent's target argument is rejected under every full-relevance injective priority, yet accepted under partial activations, one of which no VAF audience can mirror. We define the corresponding decision problem, ACTIVATION-MANIPULATION, and record baseline complexity bounds. Tight bounds and multi-agent variants are left open.

Abstract

Computational Argumentation

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