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

# Strategic Perspective Activation in Context-Dependent Argumentation
Source: [https://arxiv.org/html/2605.31581](https://arxiv.org/html/2605.31581)
Jarosław A\. Chudziak1 \\affiliations1Warsaw University of Technology \\emails\{albert\.sadowski\.stud, jaroslaw\.chudziak\}@pw\.edu\.pl

###### 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 setρ\\rhoand a priorityπ\\pi\. 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\.

## 1Introduction

Consider a team proposing an architectural change to a production service\. The proposal accumulates arguments about latency, operational complexity, deployment cost, and regression risk\. These claims are not in dispute as facts; what is in dispute is how they bear on the decision\. To a performance reviewer, latency dominates and complexity is secondary\. A reliability reviewer reads the same arguments through incident risk, and is unmoved by latency improvements without stability evidence\. The finance reviewer cares about deployment and headcount cost\. The arguments and their conflicts are fixed across reviewers\. Which attacks succeed depends on which lens governs the review\.

The proposal sponsor has some influence over which lens applies\. They choose which review tracks to pursue, who is included in early design discussions, and which forums hear the proposal first\. They cannot change how each reviewer ranks considerations within a lens \(the reliability reviewer always prioritises stability\), but they can decide which lenses are foregrounded at all\. Influence over the regime is a strategic lever\. Standard argumentation \(?\) has no parameter for the regime\. Value\-based argumentation \(?\) comes close, since each audience produces a different defeat pattern\. But a VAF audience is a strict total order on the value set; it can rerank values, not deactivate them\. So the question of whether the agent can choose a regime that accepts their target argument is inconvenient to pose in existing formalisms\.

We propose an extension of Dung’s framework, context\-dependent argumentation frameworks \(CDAFs\), and use it to study a strategic question\. We work through an example in which the target argument is reachable only via partial\-relevance activation, an action that does not correspond to any audience choice in a value\-based framework\. We define the corresponding decision problem, ACTIVATION\-MANIPULATION, and record baseline complexity bounds\. A fuller study of the framework is beyond this paper’s scope; here we focus on the strategic angle\.

## 2Context\-Dependent Argumentation Frameworks

### General definition\.

A*context\-dependent argumentation framework*is a tuple𝖢𝖣𝖠𝖥=⟨𝒜,R,𝒞,δ⟩\\mathsf\{CDAF\}=\\langle\\mathcal\{A\},R,\\mathcal\{C\},\\delta\\ranglewhere𝒜\\mathcal\{A\}is a finite set of arguments,R⊆𝒜×𝒜R\\subseteq\\mathcal\{A\}\\times\\mathcal\{A\}is the attack relation,𝒞\\mathcal\{C\}is a finite set of contexts, andδ:𝒞×R→\{0,1\}\\delta\\colon\\mathcal\{C\}\\times R\\to\\\{0,1\\\}is the*defeat function*\. For each contextc∈𝒞c\\in\\mathcal\{C\}, the*induced framework*is𝖠𝖥c=⟨𝒜,Rc⟩\\mathsf\{AF\}\_\{c\}=\\langle\\mathcal\{A\},R\_\{c\}\\ranglewithRc=\{\(a,b\)∈R:δ​\(c,\(a,b\)\)=1\}R\_\{c\}=\\\{\(a,b\)\\in R:\\delta\(c,\(a,b\)\)=1\\\}\. Since each𝖠𝖥c\\mathsf\{AF\}\_\{c\}is a standard Dung framework, the classical semantics carry over per context: aσ\\sigma\-extension inccis just aσ\\sigma\-extension of𝖠𝖥c\\mathsf\{AF\}\_\{c\}\(?\), for any ofσ∈\{𝗀𝗋,𝗉𝗋𝖾𝖿,𝗌𝗍𝖻,𝖼𝗈𝗆𝗉\}\\sigma\\in\\\{\\mathsf\{gr\},\\mathsf\{pref\},\\mathsf\{stb\},\\mathsf\{comp\}\\\}\. We writeσ​\(c\)\\sigma\(c\)for the set ofσ\\sigma\-extensions of𝖠𝖥c\\mathsf\{AF\}\_\{c\}\.

### Perspective\-labeled CDAFs\.

In the specialisation we use throughout the paper, the defeat function is derived rather than given\. Every argument carries a source perspective\. A context activates some subset of perspectives and ranks them by priority\. Defeat then follows from these assignments\.

###### Definition 1\(Perspective\-labeled CDAF\)\.

A*perspective\-labeled CDAF*is a tuple⟨𝒜,R,𝒞,Π,𝑠𝑟𝑐,ρ,π⟩\\langle\\mathcal\{A\},R,\\mathcal\{C\},\\Pi,\\mathit\{src\},\\rho,\\pi\\ranglewithΠ\\Pia finite set of perspectives,𝑠𝑟𝑐:𝒜→Π\\mathit\{src\}\\colon\\mathcal\{A\}\\to\\Piassigning each argument to its source,ρ:𝒞→2Π\\rho\\colon\\mathcal\{C\}\\to 2^\{\\Pi\}giving the active perspectives in each context, andπ:𝒞×Π→ℕ\\pi\\colon\\mathcal\{C\}\\times\\Pi\\to\\mathbb\{N\}a priority function\. The defeat function is

δπ​\(c,\(a,b\)\)=1​iff𝑠𝑟𝑐​\(a\)∈ρ​\(c\)∧π​\(c,𝑠𝑟𝑐​\(a\)\)≥π​\(c,𝑠𝑟𝑐​\(b\)\)\.\\begin\{split\}\\delta\_\{\\pi\}\(c,\(a,b\)\)=1\\;\\;\\text\{iff\}\\;\\;&\\mathit\{src\}\(a\)\\in\\rho\(c\)\\\\ &\\wedge\\pi\(c,\\mathit\{src\}\(a\)\)\\geq\\pi\(c,\\mathit\{src\}\(b\)\)\.\\end\{split\}

The condition gates only the attacker:𝑠𝑟𝑐​\(a\)∈ρ​\(c\)\\mathit\{src\}\(a\)\\in\\rho\(c\)is required, while𝑠𝑟𝑐​\(b\)\\mathit\{src\}\(b\)is not\. Deactivating a perspective therefore removes the attacks its arguments*mount*, but their priority is still counted when they are*targeted*, and the arguments themselves remain present and eligible for acceptance\. This asymmetry is what lets a perspective be silenced as an attacker while its arguments are still defended and accepted; see Table[2](https://arxiv.org/html/2605.31581#S3.T2), where\(b,t\)\(b,t\)stays active even thoughtt’s perspectiveα\\alphais inactive\.

### Comparison to VAFs and the action space\.

Perspectives are loosely analogous to values, and\(ρ,π\)\(\\rho,\\pi\)to a VAF audience\. The differences are thatπ\\pimay rerank perspectives across contexts, and thatρ\\rhomay deactivate them outright\. The second is what drives the strategic story of this paper\. We readρ\\rhoas the agent’s action space: the lens through which they choose to have arguments evaluated\. The priorityπ\\piis institutional structure that the agent cannot directly change, the ranking each lens imposes once selected\. We take the action space to be the*nonempty*subsets ofΠ\\Pi: an emptyρ\\rhoactivates no attack and would accept every argument vacuously, which we read as the absence of any evaluative regime rather than a lens the agent could select\. The example of Section[3](https://arxiv.org/html/2605.31581#S3)shows that, for a fixedπ\\pi, varyingρ\\rhoalone can be the only way for the agent to have their target argument accepted\. Throughout Sections[3](https://arxiv.org/html/2605.31581#S3)and[4](https://arxiv.org/html/2605.31581#S4)we work with a single contextcc, and accordingly writeρ\\rhoforρ​\(c\)⊆Π\\rho\(c\)\\subseteq\\Piandπ​\(⋅\)\\pi\(\\cdot\)forπ​\(c,⋅\)\\pi\(c,\\cdot\)\.

## 3A Worked Example

### Setup\.

Let𝒜=\{a,b,t,d\}\\mathcal\{A\}=\\\{a,b,t,d\\\},Π=\{α,β,γ\}\\Pi=\\\{\\alpha,\\beta,\\gamma\\\},𝑠𝑟𝑐​\(a\)=𝑠𝑟𝑐​\(t\)=α\\mathit\{src\}\(a\)=\\mathit\{src\}\(t\)=\\alpha,𝑠𝑟𝑐​\(b\)=β\\mathit\{src\}\(b\)=\\beta,𝑠𝑟𝑐​\(d\)=γ\\mathit\{src\}\(d\)=\\gamma, andR=\{\(a,t\),\(b,t\),\(a,b\),\(b,a\),\(d,b\)\}R=\\\{\(a,t\),\(b,t\),\(a,b\),\(b,a\),\(d,b\)\\\}\. Table[1](https://arxiv.org/html/2605.31581#S3.T1)summarises the structure\.

ArgumentPerspectiveAttacked byAttacksaaα\\alphabbt,bt,bbbβ\\betaa,da,dt,at,attα\\alphaa,ba,b—ddγ\\gamma—bbTable 1:Argument structure of the worked example\.The point of the construction is thataaandttshare a perspective, so the attack\(a,t\)\(a,t\)is intra\-perspective\. The agent’s goal is to havettaccepted under the preferred semantics\.

### Result 1:ttis rejected under full relevance\.

For every injectiveπ:Π→ℕ\\pi\\colon\\Pi\\to\\mathbb\{N\},ttis not credulously preferred\-accepted in the framework induced byρ=Π\\rho=\\Pi\.

Proof\.Withρ=Π\\rho=\\Pi,\(a,t\)\(a,t\)is active under every injectiveπ\\pi, sinceπ​\(α\)≥π​\(α\)\\pi\(\\alpha\)\\geq\\pi\(\\alpha\)holds trivially\. SupposeEEis admissible and containstt\. ThenEEmust defendttagainstaa, and the only attacker ofaaisbb, sob∈Eb\\in Eand\(b,a\)\(b,a\)must be active\. Injectivity forcesπ​\(β\)\>π​\(α\)\\pi\(\\beta\)\>\\pi\(\\alpha\), but this also activates\(b,t\)\(b,t\), sobbdefeatsttand\{b,t\}⊆E\\\{b,t\\\}\\subseteq Eviolates conflict\-freeness\. Conversely, ifπ​\(α\)\>π​\(β\)\\pi\(\\alpha\)\>\\pi\(\\beta\), then\(b,a\)\(b,a\)is inactive andttcannot be defended againstaa\. Either way, no admissible set containstt\. The priority ofγ\\gammais irrelevant:ddattacks onlybb, notaa\.∎

### Result 2:ttis accepted underρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}\.

Withπ​\(α\)=1\\pi\(\\alpha\)=1,π​\(β\)=2\\pi\(\\beta\)=2,π​\(γ\)=3\\pi\(\\gamma\)=3, andρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}, the set\{a,d,t\}\\\{a,d,t\\\}is a preferred extension of the induced framework, sottis credulously preferred\-accepted\.

Proof\.Computingδπ\\delta\_\{\\pi\}underρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}gives the activations in Table[2](https://arxiv.org/html/2605.31581#S3.T2)\. The active defeats are\{\(b,t\),\(b,a\),\(d,b\)\}\\\{\(b,t\),\(b,a\),\(d,b\)\\\}\.

Table 2:Active defeats underρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}\.The argumentddhas no active attacker and defeatsbb, so it defends bothaaandttagainst the only active attacker either has\. Since\(a,t\)\(a,t\)is no longer active,aaandttare not in conflict\. The set\{a,d,t\}\\\{a,d,t\\\}is conflict\-free, every member is defended bydd, and addingbbcreates a conflict with all three\. Hence\{a,d,t\}\\\{a,d,t\\\}is preferred andttis accepted\.∎

Under any full\-relevance evaluation,ttis caught in a structural trap\. Its same\-perspective neighbouraaattacks it, and the only argument that can defendttagainstaaisbb, which itself attackstt\. Wheneverbbis strong enough to defeataa, it is also strong enough to defeattt\. The defender doubles as an attacker, and the trap holds for every injective priority\. The agent’s way out is to deactivateα\\alpha\. Settingρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}silences every attack from anα\\alpha\-perspective argument, including the friendly\-fire attack\(a,t\)\(a,t\)\. The price is thataaloses its offensive capability againstbb, but the trap is now broken:dd, unaffected by the move sinceγ∈ρ\\gamma\\in\\rho, defeatsbband clears the only remaining threat tott\. This is the strategically interesting case, sincettis still under the active attack\(b,t\)\(b,t\)and is accepted only becausedddefends it; deactivatingα\\alphadoes not simply removett’s attackers\. The following proposition states the existence claim in general form\.

###### Proposition 1\.

There exists a perspective\-labeled CDAF⟨𝒜,R,Π,𝑠𝑟𝑐⟩\\langle\\mathcal\{A\},R,\\Pi,\\mathit\{src\}\\rangleand a target argumentt∈𝒜t\\in\\mathcal\{A\}such that

- \(i\)for every injective priorityπ:Π→ℕ\\pi\\colon\\Pi\\to\\mathbb\{N\},ttis not credulously preferred\-accepted under full relevanceρ=Π\\rho=\\Pi;
- \(ii\)for some priorityπ\\piand some nonemptyρ⊊Π\\rho\\subsetneq\\Pi,ttis credulously preferred\-accepted\.

Proof\.Take𝒜,R,Π,𝑠𝑟𝑐\\mathcal\{A\},R,\\Pi,\\mathit\{src\}as in the setup\. Clause \(i\) is Result 1; clause \(ii\) is Result 2 withπ​\(α\)=1\\pi\(\\alpha\)=1,π​\(β\)=2\\pi\(\\beta\)=2,π​\(γ\)=3\\pi\(\\gamma\)=3, andρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}\.∎

The same example also rules out a VAF rendering of one of the agent’s winning moves\. Consider the activationρ=\{γ\}\\rho=\\\{\\gamma\\\}, with the same priority\. Now\(a,t\)\(a,t\),\(b,t\)\(b,t\),\(a,b\)\(a,b\), and\(b,a\)\(b,a\)are all inactive, since neitherα\\alphanorβ\\betalies inρ\\rho\. Only\(d,b\)\(d,b\)remains active, so\{a,d,t\}\\\{a,d,t\\\}is again the preferred extension andttis accepted\. Both directions of the mutual attack betweenaaandbbfail to be active underρ=\{γ\}\\rho=\\\{\\gamma\\\}, and that is what no VAF audience can do\.

###### Observation 1\.

The defeat pattern induced byρ=\{γ\}\\rho=\\\{\\gamma\\\}in the framework above is not realisable as any audience of any VAF over𝒜\\mathcal\{A\}\.

Proof\.LetVVbe a value set and𝑣𝑎𝑙:𝒜→V\\mathit\{val\}\\colon\\mathcal\{A\}\\to Vany value assignment, and consider any audience, that is, any strict total order onVV\. If𝑣𝑎𝑙​\(a\)=𝑣𝑎𝑙​\(b\)\\mathit\{val\}\(a\)=\\mathit\{val\}\(b\), then both\(a,b\)\(a,b\)and\(b,a\)\(b,a\)are intra\-value attacks and succeed in every audience \(?\)\. If𝑣𝑎𝑙​\(a\)≠𝑣𝑎𝑙​\(b\)\\mathit\{val\}\(a\)\\neq\\mathit\{val\}\(b\), the strict total order satisfies exactly one of𝑣𝑎𝑙​\(a\)≻𝑣𝑎𝑙​\(b\)\\mathit\{val\}\(a\)\\succ\\mathit\{val\}\(b\)or𝑣𝑎𝑙​\(b\)≻𝑣𝑎𝑙​\(a\)\\mathit\{val\}\(b\)\\succ\\mathit\{val\}\(a\), so exactly one of the two directions succeeds\. In neither case do both directions fail\. So the defeat pattern underρ=\{γ\}\\rho=\\\{\\gamma\\\}is not realisable as a VAF audience, regardless of the value assignment\.∎

In the perspective\-labeled formalism, the agent picksρ\\rho, not the source assignment\. So even if some other choice of values were to recover the strategically natural moveρ=\{β,γ\}\\rho=\\\{\\beta,\\gamma\\\}within VAF expressiveness, the moveρ=\{γ\}\\rho=\\\{\\gamma\\\}remains available to the agent and falls outside what any VAF audience can do\.

## 4Activation Manipulation

The strategic question of the previous section generalises to a decision problem\. Given a perspective\-labeled framework, a fixed priority, and a target argument, does the agent have any choice ofρ\\rhothat accepts the target?

Activation\-Manipulationσ\. Input\.A finite tuple⟨𝒜,R,Π,𝑠𝑟𝑐⟩\\langle\\mathcal\{A\},R,\\Pi,\\mathit\{src\}\\rangle, a priorityπ:Π→ℕ\\pi\\colon\\Pi\\to\\mathbb\{N\}, and a target argumentt∈𝒜t\\in\\mathcal\{A\}\. Question\.Does there exist a nonemptyρ⊆Π\\rho\\subseteq\\Pisuch thatttis credulouslyσ\\sigma\-accepted in the framework induced by\(ρ,π\)\(\\rho,\\pi\)?

For the upper bound we use a standard guess\-and\-check\. Nondeterministically choose a nonemptyρ⊆Π\\rho\\subseteq\\Pi, then verifyσ\\sigma\-acceptance in the induced framework\. The verification cost depends onσ\\sigma: polynomial for grounded, and in NP for stable \(guess a stable extension containingtt\)\.

The preferred case looks harder at first\. Verifying that a set is a preferred extension requires checking maximality, that no admissible superset exists, which is co\-NP, suggesting an overallΣ2p\\Sigma\_\{2\}^\{p\}bound\. The escape is a standard fact: credulous preferred\-acceptance coincides with credulous admissibility, since every admissible set extends to some preferred extension\. So it suffices to find an admissible set containingtt, and we can guessρ\\rhoand the admissible witness together in a single NP computation\.

Together with the existential guess ofρ\\rho, this keepsActivation\-Manipulationprefin NP\. Soρ\\rhoand a witness extension can be guessed jointly and verified in polynomial time, placingActivation\-Manipulationσin NP forσ∈\{𝗀𝗋,𝗌𝗍𝖻,𝗉𝗋𝖾𝖿\}\\sigma\\in\\\{\\mathsf\{gr\},\\mathsf\{stb\},\\mathsf\{pref\}\\\}\. For lower bounds, setΠ=\{π0\}\\Pi=\\\{\\pi\_\{0\}\\\}with all arguments mapped to the single perspective andπ\\pitrivially fixed\. Sinceρ\\rhomust be nonempty andΠ\\Piis a singleton, the only admissible activation isρ=\{π0\}\\rho=\\\{\\pi\_\{0\}\\\}, under which every attack is active, so the induced framework is exactly the input Dung framework and the problem reduces to credulousσ\\sigma\-acceptance in standard Dung\. This yields NP\-hardness forσ∈\{𝗌𝗍𝖻,𝗉𝗋𝖾𝖿\}\\sigma\\in\\\{\\mathsf\{stb\},\\mathsf\{pref\}\\\}\(?;?\), soActivation\-Manipulationσis NP\-complete in those cases\. Credulous grounded acceptance is in P, so the same reduction gives only P\-hardness for grounded\. Whether the freedom to chooseρ\\rhoraises the grounded variant to NP\-completeness is open\.

The restriction to nonemptyρ\\rhois essential to these bounds\. An empty activation deactivates every attack, so the induced framework has𝒜\\mathcal\{A\}as its unique extension under eachσ∈\{𝗀𝗋,𝗌𝗍𝖻,𝗉𝗋𝖾𝖿\}\\sigma\\in\\\{\\mathsf\{gr\},\\mathsf\{stb\},\\mathsf\{pref\}\\\}and accepts every argument; allowing it would make the problem trivially positive and break the reduction, since the constructed instance would answer “yes” regardless of whetherttis credulously accepted in the input\. Even among nonempty activations many instances stay easy: if some perspective is the source of no attacker oftt, then forσ∈\{𝗀𝗋,𝗉𝗋𝖾𝖿\}\\sigma\\in\\\{\\mathsf\{gr\},\\mathsf\{pref\}\\\}activating only that perspective leavesttunattacked, hence accepted\. The hardness above therefore comes from instances in whichttcannot be isolated in this way, as in the single\-perspective reduction, where the sole nonempty activation reinstates every attack\.

Several variants of the problem are not addressed here\. The activationρ\\rhomay be further constrained, for instance by requiring some perspectives to remain active or by attaching a cost to each activation; such constraints are also what block the cheap isolation move above and make the general problem robustly nontrivial\. The priorityπ\\pimay itself be a choice variable, which enlarges the action space\. In a multi\-agent version, several agents pick disjoint or overlapping subsets ofΠ\\Pi, with the realisedρ\\rhoformed by union or intersection; this yields natural game\-theoretic refinements with cooperative and adversarial variants, including the existence of strategic equilibria in which no agent can unilaterally redirect the outcome by altering its share ofρ\\rho\. The skeptical version, asking whether someρ\\rhoacceptsttin everyσ\\sigma\-extension, is also open\.

## 5Discussion

The strategic action we study here, varying which attacks constitute defeats while keeping the argument structure fixed, has three close neighbours\. Control argumentation frameworks \(?\) let an agent choose between alternative argument and attack sets so that a target is accepted under uncertainty about the framework’s structure; here, the structure is fixed and only the defeat function varies\. Manipulation in incomplete argumentation \(?\) is the closest of the three, since both ask whether an agent can drive a target to acceptance via a structural choice, and a careful comparison is left for future work\. Value\-based argumentation \(?\) is the closest formal kin, and the example of Section[3](https://arxiv.org/html/2605.31581#S3)sharpens the difference: a VAF audience can rerank values but cannot deactivate one, so the strategic options it offers are strictly fewer than those of perspective activation\. Other extensions of Dung’s theory modulate defeat through meta\-level argumentation \(?\) or per\-node acceptance conditions \(?\), but in each case the modulation is endogenous or fixed at definition time, and none treats activation as an action available to the agent\. Beyond these formal neighbours, applied multi\-agent and LLM\-based systems operationalise argumentation as explicit debate among agents, for instance, dialectical refinement for argument\-component classification \(?\)\. Such systems fix neither an attack relation nor a defeat function explicitly, working at a different level of abstraction from the framework here, and the strategic question we raise is orthogonal to their design\.

Several questions remain open\. Tight complexity bounds forActivation\-Manipulation, especially for the grounded variant, are unsettled\. There are mechanism\-design questions when the agent’s choice ofρ\\rhois institutionally constrained, for instance when certain perspectives are mandatory or when activations carry cost\. The multi\-agent setting, where several agents jointly determineρ\\rhounder cooperative or adversarial dynamics, is the most direct extension of the present work and, we think, the most productive direction for further study; the existence of strategic equilibria under such dynamics is a natural question there\. Whether the phenomenon arises in larger or applied frameworks is also open \- multi\-perspective agent memory, where the same experience receives goal\-conditioned encodings reconciled by argumentation at retrieval \(?\), is one such setting\.

## References