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在认识论层面的应用，不仅扩展了标准认识逻辑以捕捉主体拥有的信息，还包含了他们感兴趣的问题。我们采用[Ciardelli/Otto: JSL 2021]中提出的InqML框架下自然的互模拟等价概念，将InqML的表达能力刻画为在探究性认识（类S5）模型的关系编码所形成的自然类双排序一阶结构上的一阶逻辑的互模拟不变片段。这些结构类本质上的非初等性，无论我们旨在经典模型论还是有限模型论框架下进行刻画，都要求采用非经典的模型论方法分析一阶逻辑的表达能力。