Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states, and characterise inquisitive modal logic as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures.

中文翻译：

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好奇的双向模拟

好奇的模态逻辑，InqML, 是标准 Kripke 式模态逻辑的概括。在其认知化身中，它扩展了标准认知逻辑，不仅可以捕获代理拥有的信息，还可以捕获他们感兴趣的问题。从技术上讲，InqML适合基于团队语义的逻辑系列。从模型理论的角度来看，它使我们朝着一元二阶逻辑的方向迈出了一步，因为好奇的模态运算符涉及对世界集的量化。我们在InqML. 我们比较表现力InqML和一阶逻辑在具有两种类型的关系结构的上下文中，一种用于世界，一种用于信息状态，并将好奇模态逻辑描述为一阶逻辑在各种自然类的二分类结构上的互模拟不变片段。