The aim of this paper is to study the complexity of the model checking problem MC for inquisitive propositional logic InqB and for inquisitive modal logic InqM, that is, the problem of deciding whether a given finite structure for the logic satisfies a given formula. In recent years, this problem has been thoroughly investigated for several variations of dependence and teams logics, systems closely related to inquisitive logic. Building upon some ideas presented by Yang, we prove that the model checking problems for InqB and InqM are both AP-complete.

翻译：本文旨在研究探究性命题逻辑InqB与探究性模态逻辑InqM的模型检测问题MC的复杂度，即判定给定逻辑的有限结构是否满足给定公式的问题。近年来，该问题已在依赖逻辑与团队逻辑的多种变体（与探究性逻辑密切相关的系统）中得到深入研究。基于Yang提出的若干思想，我们证明InqB与InqM的模型检测问题均为AP-完全问题。