Inquisitive Action Logic

2026-06-30

AI Summary

This study addresses the limitations of traditional action logics in capturing how agents determine outcomes through their actions. It proposes InqAL, a multi-agent modal logic that integrates inquisitive logic with action efficacy for the first time, formalizing the notion of “agent determinacy” within concurrent game structures. By employing an inquisitive neighborhood semantics, a sound and complete axiomatization, and a representation theorem, the framework precisely characterizes realizable effectivity functions. The work establishes the completeness of InqAL’s axiom system, proves that the logic enjoys the finite model property and is decidable, and provides necessary and sufficient conditions for neighborhood frames to originate from concurrent game structures.

Abstract

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.

Problem

• inquisitive logic
• action logic
• multi-agent systems
• agentive determination
• modal logic

Innovation

• inquisitive action logic
• agentive determination
• concurrent game structures
• multi-agent modal logic
• finite model property