探究性互模拟
Inquisitive bisimulation
AI总结：
本文引入并研究探究性模态逻辑InqML中的互模拟等价，将其刻画为双类型结构上一阶逻辑的互模拟不变片段，并比较其与一阶逻辑的表达能力。
摘要：
探究性模态逻辑InqML是标准克里普克式模态逻辑的推广。在其认识论形式中，它扩展了标准认识逻辑，不仅捕捉智能体拥有的信息，还捕捉它们感兴趣的问题。从技术上讲，InqML属于基于团队语义的逻辑家族。从模型论的角度来看，它朝着一元二阶逻辑的方向迈出了一步，因为探究性模态算子涉及对世界集合的量词化。我们引入并研究了InqML中互模拟等价这一自然概念。我们在具有两种类型的关系结构（一种用于世界，一种用于信息状态）的背景下比较了InqML和一阶逻辑的表达能力。我们将探究性模态逻辑及其多智能体认识S5类变体刻画为各种自然类别的双类型结构上的一阶逻辑的互模拟不变片段。这些结果关键性地需要非经典方法来研究互模拟和非初等类结构上的一阶表达性，无论我们是旨在经典模型理论还是有限模型理论意义上的刻画。
英文摘要：
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. We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. These results crucially require non-classical methods in studying bisimulation and first-order expressiveness over non-elementary classes of structures, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory.
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