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This research advances formal argumentation theory by modeling how procedural contexts dynamically alter defeat relations, moving beyond static audience-based values to capture real-world regulatory or stage-specific constraints. The study provides a polynomial-time decision procedure for determining if such context-dependent frameworks can be reduced to simpler value-based models and empirically demonstrates that representability is rare as the number of contexts increases. These findings are significant for developers building robust AI reasoning systems, particularly those requiring dynamic compliance checks or multi-stage debate simulations where rules shift based on environment rather than just preference ordering.
From Contexts to Values: Context-Dependent Defeat in Abstract Argumentation
arXiv:2608.15536v1 Announce Type: new 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 set of arguments, 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: is context genuinely new, or 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 $\Sigma^p_3$. We also present a validated reference implementation and a measurement: representability is rare and falls fast with the number of contexts.
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 set of arguments, 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: is context genuinely new, or 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 $\Sigma^p_3$. We also present a validated reference implementation and a measurement: representability is rare and falls fast with the number of contexts.
Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO)
arXiv:2608.15536 [cs.AI]
(or arXiv:2608.15536v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.15536 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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