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

We introduce inquisitive action logic, InqAL, a multi-agent modal logic for reasoning about action. While traditional approaches focus on what properties of the outcome an agent can force, InqAL also captures what aspects of the outcome an agent determines through their actions. As we argue, such claims of agentive determination are naturally analyzed as modal claims involving questions. Technically, InqAL is a multi-agent extension of inquisitive neighborhood logic based on concurrent game structures. With respect to statements, it is expressively equivalent to the individual-agent fragment of the socially friendly coalition logic recently proposed by Goranko and Enqvist. We present an axiomatization of InqAL and prove completeness and decidability via the finite model property. Along the way, we establish a representation theorem for actual effectivity functions, associating to an agent the sets of outcomes corresponding to their possible actions; we give exact conditions under which a multi-agent neighborhood frame arises from a concurrent game structure.

Reasoning about what agents can achieve through strategic interaction is a core challenge in Multi-Agent Systems (MAS). Logics for strategic ability, such as ATL, provide rigorous methods, but their adoption is often hindered by the computational cost of strategy synthesis. We introduce a neuro-symbolic framework that integrates large language models (LLMs) into the model-checking pipeline for MAS. The LLM acts as a strategy-generation oracle, proposing candidate strategies that are then formally validated by a standard MAS model checker. This generate-and-certify architecture uses LLM guidance to navigate large combinatorial strategy spaces while preserving formal soundness: generated strategies are accepted only when certified by the verifier. We instantiate the framework for bounded strategic reasoning in NatATL and introduce the first NatATL strategy-synthesis dataset, consisting of 4211 instances. Experiments with an open-weight Qwen3-32B model show that our certified pipeline achieves 92% accuracy on strategy-synthesis outcomes.

Existing approaches to multi-agent belief combination have established mature foundations for combining uncertain beliefs under common assumptions: consensus methods use iterative averaging, logic-based methods resolve conflicting knowledge bases, and epistemic logic analyzes agents' information states. Typically, these approaches assume that the structure determining what each agent can represent remains fixed. However, in many scenarios, agents gain or lose observational capacity during execution, and what was once admissible may become structurally impossible. This paper presents a formal framework for handling such runtime changes in epistemic partitions over continuous belief profiles. A hybrid approach exploits the advantages of answer set programming in elaboration tolerance, declarative integrity constraints, and explanations, with the numerical flexibility of Python. The framework applies to domains where agents operate at heterogeneous and possibly changing levels of resolution, and provides formal guarantees of admissibility preservation under refinement, unique mass-preserving repair under coarsening, and explanation completeness. Evaluation across 100 randomly generated topology changes confirms complete violation detection and explanation coverage.