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

Abstract: 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.

• The paper introduces context-dependent argumentation frameworks, where agents activate perspectives that determine which attacks succeed while preserving classical Dung semantics within each context.
• The paper demonstrates that partial activation can make a target credulously accepted even when every full-relevance injective priority rejects it, and can produce defeat patterns no value-based argumentation framework can represent.
• The paper proves Activation-Manipulation is NP-complete under stable and preferred semantics, while grounded acceptance is in P and P-hard, leaving its exact complexity and several strategic variants open.

Motivation and problem

Standard abstract argumentation treats the attack relation and its defeat interpretation as fixed. In many practical settings, however, the same arguments and conflicts are evaluated under different evaluative regimes — different review lenses, institutional priorities, or audience perspectives — and an agent may hold some influence over which regime applies. The paper "Choosing the Lens: Strategic Perspective Activation in Context-Dependent Argumentation" (2605.31581) formalizes this situation. The authors observe that value-based argumentation frameworks (VAFs) come closest to capturing regime-dependence, since each audience induces a different defeat pattern, but a VAF audience is a strict total order over the value set: it can rerank values but never deactivate one. Consequently, the question "can the agent choose a regime under which their target argument is accepted?" cannot be posed naturally in existing formalisms.

Context-dependent argumentation frameworks

The paper introduces the context-dependent argumentation framework (CDAF), a tuple $\langle A, R, C, \delta \rangle$ where $\delta \colon C \times R \to \{0,1\}$ determines, per context, which attacks succeed. Each context induces a standard Dung framework, so classical semantics (grounded, preferred, stable, complete) carry over per context unchanged.

The operative specialisation is the perspective-labeled CDAF. Each argument carries a source perspective via $\mathit{src} \colon A \to \mathcal{P}$, and a context specifies a relevance set $\rho \subseteq \mathcal{P}$ of activated perspectives together with a priority function $\pi \colon C \times \mathcal{P} \to \mathbb{N}$. An attack succeeds iff the attacker's source is active and its priority is at least that of the target's source:

$$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$

The asymmetry is deliberate: only the attacker must be active. Deactivating a perspective removes its offensive capability while its arguments remain present, still defended, and still eligible for acceptance. The paper reads $\rho$ as the agent's action space (the lens it selects) and $\pi$ as institutional structure the agent cannot change. The empty activation is excluded, since it accepts every argument vacuously and represents the absence of any evaluative regime.

The worked example and the expressiveness gap

The central construction uses four arguments $\{a, b, t, d\}$ over three perspectives, with $t$ the agent's target. Arguments $\delta \colon C \times R \to \{0,1\}$0 and $\delta \colon C \times R \to \{0,1\}$1 share perspective $\delta \colon C \times R \to \{0,1\}$2, making $\delta \colon C \times R \to \{0,1\}$3 an intra-perspective attack; $\delta \colon C \times R \to \{0,1\}$4 (perspective $\delta \colon C \times R \to \{0,1\}$5) mutually attacks $\delta \colon C \times R \to \{0,1\}$6 and also attacks $\delta \colon C \times R \to \{0,1\}$7; $\delta \colon C \times R \to \{0,1\}$8 (perspective $\delta \colon C \times R \to \{0,1\}$9) attacks only $\mathit{src} \colon A \to \mathcal{P}$0.

The paper establishes two contrasting results. First, under full relevance $\mathit{src} \colon A \to \mathcal{P}$1, $\mathit{src} \colon A \to \mathcal{P}$2 is rejected under every injective priority $\mathit{src} \colon A \to \mathcal{P}$3. The argument is a structural trap: $\mathit{src} \colon A \to \mathcal{P}$4 can only be defended against $\mathit{src} \colon A \to \mathcal{P}$5 by $\mathit{src} \colon A \to \mathcal{P}$6, but injectivity forces $\mathit{src} \colon A \to \mathcal{P}$7 whenever $\mathit{src} \colon A \to \mathcal{P}$8 is active, and the same inequality activates $\mathit{src} \colon A \to \mathcal{P}$9, so the defender doubles as an attacker and any admissible set containing $\rho \subseteq \mathcal{P}$0 violates conflict-freeness. Second, under partial activation $\rho \subseteq \mathcal{P}$1 with priorities $\rho \subseteq \mathcal{P}$2, the set $\rho \subseteq \mathcal{P}$3 is a preferred extension, so $\rho \subseteq \mathcal{P}$4 is credulously accepted. Deactivating $\rho \subseteq \mathcal{P}$5 silences the friendly-fire attack $\rho \subseteq \mathcal{P}$6 and simultaneously disarms $\rho \subseteq \mathcal{P}$7 against $\rho \subseteq \mathcal{P}$8; $\rho \subseteq \mathcal{P}$9, whose perspective remains active, defeats $\pi \colon C \times \mathcal{P} \to \mathbb{N}$0 and defends $\pi \colon C \times \mathcal{P} \to \mathbb{N}$1. Notably, $\pi \colon C \times \mathcal{P} \to \mathbb{N}$2 is still under the active attack $\pi \colon C \times \mathcal{P} \to \mathbb{N}$3 — acceptance comes from defense, not from removing all attackers. These results jointly establish the paper's general existence claim: some perspective-labeled CDAFs admit targets rejected under all full-relevance injective priorities yet accepted under a partial activation.

A stronger expressiveness result follows. Under the activation $\pi \colon C \times \mathcal{P} \to \mathbb{N}$4, both directions of the mutual attack between $\pi \colon C \times \mathcal{P} \to \mathbb{N}$5 and $\pi \colon C \times \mathcal{P} \to \mathbb{N}$6 fail, yet $\pi \colon C \times \mathcal{P} \to \mathbb{N}$7 is still accepted. The paper proves this defeat pattern is not realisable by any audience of any VAF over the same arguments, regardless of value assignment: in a VAF, intra-value attacks succeed in every audience, and inter-value attacks succeed in exactly one direction under a strict total order, so both directions of a mutual attack can never simultaneously fail. This is a concrete separation: perspective activation offers strategic options strictly outside VAF expressiveness, and the winning move $\pi \colon C \times \mathcal{P} \to \mathbb{N}$8 remains available to the agent even if some value assignment could recover the $\pi \colon C \times \mathcal{P} \to \mathbb{N}$9 case.

The Activation-Manipulation problem

The strategic question generalises to the decision problem Activation-Manipulation$$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$0: given the framework, a fixed priority $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$1, and target $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$2, does some nonempty $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$3 exist under which $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$4 is credulously $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$5-accepted? The paper records baseline complexity bounds:

Semantics $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$6	Upper bound	Lower bound	Status
Grounded	P (credulous grounded acceptance)	P-hard	Open whether NP-complete
Stable	NP	NP-hard	NP-complete
Preferred	NP	NP-hard	NP-complete

Two observations make the NP upper bounds work. For preferred semantics, credulous preferred-acceptance coincides with credulous admissibility (every admissible set extends to a preferred one), so the $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$7-looking maximality check collapses into a single NP guess of $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$8 together with an admissible witness. For the lower bound, collapsing all arguments onto a single perspective forces the unique nonempty activation to reinstate every attack, reducing standard credulous $$\delta_\pi(c, (a,b)) = 1 \iff \mathit{src}(a) \in \rho(c) \wedge \pi(c, \mathit{src}(a)) \geq \pi(c, \mathit{src}(b)).$$9-acceptance to the problem.

The paper is careful about the boundaries of these bounds. The restriction to nonempty $\rho$0 is essential — allowing the empty activation would make every instance trivially positive and break the reduction. Moreover, many nonempty instances remain easy: if some perspective sources no attacker of $\rho$1, activating only that perspective isolates $\rho$2 and yields immediate acceptance under grounded or preferred semantics. The hardness therefore stems precisely from instances where the target cannot be cheaply isolated.

Relation to neighbouring formalisms

The paper positions activation manipulation against three neighbours. Control argumentation frameworks let an agent choose among alternative argument and attack sets under structural uncertainty; here the structure is fixed and only the defeat function varies. Manipulation in incomplete argumentation frameworks is identified as the closest relative — both ask whether a structural choice can drive a target to acceptance — but a detailed comparison is explicitly deferred. VAFs are the closest formal kin, and the example sharpens their limitation: an audience reranks but cannot deactivate. Other extensions that modulate defeat (meta-level argumentation, abstract dialectical frameworks) fix the modulation at definition time or make it endogenous; none treats activation as an agent's action. The authors also note that LLM-based debate systems operate at a different level of abstraction, fixing neither attack nor defeat relations explicitly, so the strategic question raised is orthogonal to their design.

Limitations and open questions

The paper is explicit that this is a baseline treatment. Tight complexity bounds are unsettled — in particular, whether the freedom to choose $\rho$3 lifts the grounded variant from P-hardness to NP-completeness is open, as is the skeptical version of the problem. Several variants are unaddressed: constrained activations (mandatory perspectives, activation costs), which would also block the cheap isolation move and make the general problem robustly nontrivial; $\rho$4 as a second choice variable; and multi-agent settings in which several agents pick overlapping subsets of $\rho$5 with the realised $\rho$6 formed by union or intersection, raising game-theoretic questions about cooperative and adversarial equilibria. Whether the phenomenon arises in larger or applied frameworks — for instance, multi-perspective agent memory with argumentation-driven retrieval — is also left open.

Conclusion

The paper contributes a minimal extension of Dung's framework in which regime selection becomes a strategic action, demonstrates through a compact example that partial perspective activation can succeed where every full-relevance priority fails and where no VAF audience can replicate the winning defeat pattern, and establishes NP-completeness for the stable and preferred variants of the resulting manipulation problem. Its value lies in isolating deactivation — as opposed to reranking — as the decisive strategic lever, and in mapping the baseline computational landscape against which the conceded open questions (grounded complexity, skeptical acceptance, multi-agent equilibria) can be resolved.