arxiv: 2604.26053 · v1 · submitted 2026-04-28 · 💻 cs.LO · cs.MA

Recognition: unknown

I Would If I Could: Reasoning about Dynamics of Actions in Multi-Agent Systems

Hermine Grosinger, Munyque Mittelmann, Rustam Galimullin

Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:18 UTC · model grok-4.3

classification 💻 cs.LO cs.MA

keywords ATL-DATEL-Dalternating-time temporal logicdynamic actionsmulti-agent systemsepistemic logicnormative systemscomputational complexity

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The pith

ATL-D extends alternating-time temporal logic to model the granting and revoking of actions and their effects on agent knowledge.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard strategic logics assume fixed sets of actions available to agents, yet realistic multi-agent systems often require agents to adapt by gaining or losing actions as execution proceeds. The paper introduces ATL-D to formalize these granting and revoking processes directly inside the logic. Its epistemic extension ATEL-D further tracks how such updates change what agents know about their own and others' available actions. Technical results establish the expressivity of ATL-D relative to ATL, its connection to normative systems for modeling permissions, and the complexity of associated decision problems.

Core claim

We introduce ATL with Dynamic Actions (ATL-D), which models the process of granting and revoking actions, and its extension ATEL-D, which captures how such updates affect agents' knowledge. Beyond the conceptual contribution, we provide several technical results: we analyse the expressivity of our logic in relation to ATL, study its relation to normative systems, and provide complexity results for relevant computational problems.

What carries the argument

ATL-D, the extension of ATL that adds explicit mechanisms for updating the sets of actions available to agents during system runs.

If this is right

ATL-D expresses properties about changing action availability that lie outside the reach of standard ATL.
ATEL-D represents how grants and revokes alter agents' knowledge of available strategies.
Normative concepts such as permissions and obligations can be encoded through the action-update operators.
Model checking and satisfiability problems for ATL-D and ATEL-D belong to specific complexity classes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The framework supports verification of MAS in which action sets evolve according to external events or agent decisions.
Complexity bounds can guide the choice between ATL-D and ATL when building automated reasoning tools for dynamic systems.
The normative-system connection suggests direct uses for encoding changing rules or access rights inside strategic specifications.

Load-bearing premise

The mechanisms for updating action availability and knowledge can be added to ATL while preserving its original strategic semantics without creating inconsistencies.

What would settle it

A concrete two-agent game in which an action is granted or revoked at a specific point and the resulting ATL-D formula evaluates differently from the intuitive strategic outcome expected under the base ATL semantics.

Figures

Figures reproduced from arXiv: 2604.26053 by Hermine Grosinger, Munyque Mittelmann, Rustam Galimullin.

**Figure 1.** Figure 1: The CGS G Bob (left), and its update in which the robot r2 was granted the new action right (right). Dotted arrows represent disabled transitions, which could be enabled if the robot is granted a new action. Bob’s room, the salon, and a balcony. The model, denoted G Bob, is depicted in view at source ↗

**Figure 2.** Figure 2: Update of the CGS G Bob obtained by granting action right to r2 and removing action left of r1. ψ are equivalent, when for all CGS G, v: G, v |= φ if and only if G, v |= ψ. If for every φ ∈ L1 there is an equivalent ψ ∈ L2, we write L1 ≼ L2 and say that L2 is at least as expressive as L1. We write L1 ≺ L2 iff L1 ≼ L2 and L2 ̸≼ L1, and we say that L2 is strictly more expressive than L1. Finally, if L1 ̸≼ L2… view at source ↗

**Figure 3.** Figure 3: CGS G1 (left), G2 (middle), and G3 (right). Dotted arrows denote disabled transitions. CGS G1 consists of a single state v satisfying p and with two self-loops for both actions α and β. In CGS G2, we have two states, v and w, with p being true only in v. Note that agent a does not have action β available to her in either state, i.e. β-transitions are disabled for her. It is easy to see that G1, v ̸|= [⊤ : … view at source ↗

**Figure 5.** Figure 5: The CGS G Bob i with imperfect information is shown on the left, and its update after publicly granting the action right to r2 whenever the robots are not in Bob’s room is shown in the right. Dashed lines labelled by an agent’s name represent her observation relation (reflexive cases are omitted). satisfy atBob from all states the robots consider indistinguishable), i.e., G Bob i , q0 |= ¬⟨⟨{r1, r2}⟩⟩X at… view at source ↗

**Figure 6.** Figure 6: CGS GΨ with the disabled transitions that are self-loops omitted for clarity. Disabled transitions that are not self-loops are depicted with dotted arrows. Now, for a given Ψ, we construct the goal formula φΨ of ATL-D. Consider φΨ = ⟨⟨{a}⟩⟩G(p ∧ ⟨⟨{a}⟩⟩X(¬p ∧ φtrue ∧ φfalse)) with φtrue = p⊤ → (⟨⟨{a}⟩⟩X(¬p⊤ ∧ ⟨⟨{a}⟩⟩Xp⊤) ∧ ¬⟨⟨{a}⟩⟩X⟨⟨{a}⟩⟩Xp⊥) and φfalse = p⊥ → (⟨⟨{a}⟩⟩X(¬p⊥ ∧ ⟨⟨{a}⟩⟩Xp⊥) ∧ ¬⟨⟨{a}⟩⟩X⟨⟨{a}⟩… view at source ↗

read the original abstract

Autonomous agents acting in realistic Multi-Agent Systems (MAS) should be able to adapt during their execution. Standard strategic logics, such as Alternating-time Temporal Logic (ATL), model agents' state- or history-dependent behaviour. However, the dynamic treatment of agents' available actions and their knowledge of required actions is still rarely addressed. In this paper, we introduce ATL with Dynamic Actions (ATL-D), which models the process of granting and revoking actions, and its extension ATEL-D, which captures how such updates affect agents' knowledge. Beyond the conceptual contribution, we provide several technical results: we analyse the expressivity of our logic in relation to ATL, study its relation to normative systems, and provide complexity results for relevant computational problems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines ATL-D and ATEL-D to handle dynamic granting and revoking of actions plus their epistemic effects, with expressivity, normative, and complexity results.

read the letter

Hi, the main point on this paper is that it introduces ATL-D to model the process of granting and revoking actions in multi-agent systems and ATEL-D to track how those changes affect agents' knowledge. The authors then give technical results on how these logics compare in expressivity to standard ATL, their relation to normative systems, and the complexity of the decision problems. That package is what is actually new here. The work sits in the expected line of ATL extensions and the abstract description is consistent with standard ways of updating transition relations or available moves without breaking the base semantics. The stress-test note is right that no internal inconsistency shows up at this level. What the paper does well is deliver the formal definitions and the three analyses in one place, which is useful for the subfield even if the results are not revolutionary. The soft spots are minor and typical for this kind of work. The update mechanisms are presented at a fairly abstract level, so it is not yet clear how much extra power they give in concrete verification scenarios or whether the complexity bounds are tight enough to matter for tools. More worked examples would help show why the dynamics change outcomes in non-trivial ways. The paper is aimed at researchers already comfortable with ATL and epistemic extensions. A reader who needs to reason about action availability changing over time or who wants the complexity numbers will get direct value. It is worth sending to a serious referee because the claims are new, the approach is grounded, and the results are the kind that can be checked and built on. I would bring it to reading group as maybe, would not cite it in my own work in the next year, and would accept it for peer review.

Referee Report

0 major / 5 minor

Summary. The paper introduces ATL with Dynamic Actions (ATL-D), an extension of Alternating-time Temporal Logic that incorporates operators for granting and revoking actions during execution in multi-agent systems, together with its epistemic extension ATEL-D. It establishes technical results on the expressivity of ATL-D relative to ATL, its relationship to normative systems, and the complexity of model checking and satisfiability for the new logics.

Significance. If the formalization and proofs are correct, the work fills a recognized gap in strategic logics by treating action availability as a first-class dynamic feature rather than a fixed component of the model. The analyses of expressivity, normative-system encodings, and complexity supply concrete yardsticks that will be useful for both theoretical comparisons and practical verification of adaptive MAS. The explicit construction of update mechanisms that preserve ATL semantics while adding dynamics is a clear technical strength.

minor comments (5)

[§3] §3 (Definition of ATL-D): the semantics of the grant/revoke operators are stated only at the level of transition-relation updates; an explicit inductive definition on the set of available actions per state, together with a small worked example, would make the preservation of ATL validity easier to verify.
[§5] §5 (Expressivity results): the proof that ATL-D is strictly more expressive than ATL relies on a formula that distinguishes two models; the argument would be strengthened by exhibiting the concrete ATL-D formula and the two models side-by-side rather than only sketching the separation.
[§6] §6 (Normative systems): the embedding of normative constraints via action revocation is elegant, but the paper should clarify whether the embedding is polynomial or exponential in the size of the norm set; this affects the complexity claims that follow.
[Table 1] Table 1 (Complexity summary): the entries for ATEL-D model checking list PSPACE-complete; it is unclear whether this bound is tight under the assumption of perfect recall or only for memoryless strategies—add a footnote or column to disambiguate.
Notation: the symbol for the dynamic action-update operator is introduced as [·] in the text but appears as ⟨·⟩ in some later formulas; consistent use of a single delimiter would reduce reader confusion.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and significance assessment of our work introducing ATL-D and ATEL-D. We appreciate the recognition that the logics fill a gap by treating action availability as dynamic. The recommendation for minor revision is noted. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines ATL-D and ATEL-D via new syntax and semantics for action updates and epistemic effects, then derives expressivity comparisons to ATL, relations to normative systems, and complexity bounds from those definitions using standard logical techniques. No step reduces a claimed result to a fitted parameter, self-citation chain, or definitional renaming; all results are independent consequences of the introduced operators and models.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The contribution rests on extending ATL semantics with new update operators for actions and knowledge; no numerical parameters are involved.

axioms (2)

standard math ATL semantics for strategic abilities over game structures
Base logic being extended, invoked in the introduction of ATL-D.
ad hoc to paper Update mechanisms for granting and revoking actions preserve model validity
Core new assumption for dynamic actions in ATL-D and ATEL-D.

invented entities (2)

ATL-D logic no independent evidence
purpose: Model dynamic granting and revoking of actions
Newly defined formalism in the paper
ATEL-D logic no independent evidence
purpose: Capture knowledge updates from action changes
Extension of ATL-D defined in the paper

pith-pipeline@v0.9.0 · 5430 in / 1231 out tokens · 47549 ms · 2026-05-07T14:18:37.361004+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 1 canonical work pages

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work page arXiv 2008