Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of bisimulation equivalence in the setting of InqML, as introduced in [Ciardelli/Otto: JSL 2021], to characterise the expressiveness of InqML as the bisimulation invariant fragment of first-order logic over natural classes of two-sorted first-order structures that arise as relational encodings of inquisitive epistemic (S5-like) models. The non-elementary nature of these classes crucially requires non-classical model-theoretic methods for the analysis of first-order expressiveness, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory.

翻译：探究性模态逻辑（InqML）在其认知变体中，扩展了标准认知逻辑，不仅捕捉智能体拥有的信息，还捕捉他们感兴趣的问题。我们采用[Ciardelli/Otto: JSL 2021]中引入的InqML环境下的自然互模拟等价概念，将InqML的表达能力刻画为一阶逻辑在自然类双类型一阶结构上的互模拟不变片段，这些结构作为探究性认知（类S5）模型的关系编码而出现。这些类别的非初等性质本质上要求使用非经典模型论方法来分析一阶表达能力，无论我们的目标是经典模型论意义还是有限模型论意义上的刻画。