探究式模态逻辑中的双仿真

Ivano Ciardelli, M. Otto
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引用次数: 4

摘要

探究性模态逻辑,InqML,是标准kripke风格模态逻辑的泛化。在其认识论的化身中,它扩展了标准的认识论逻辑,不仅捕获智能体拥有的信息,还捕获它们感兴趣的问题。从技术上讲,InqML适合基于团队语义的逻辑家族。从模型理论的角度来看,它使我们在一元二阶逻辑的方向上迈出了一步,因为好奇模态算子涉及对世界集合的量化。我们引入并研究了InqML环境中双模拟等价的自然概念。我们比较了InqML和一阶逻辑的表达性,并将探究性模态逻辑描述为各种两排序关系结构上一阶逻辑的双模拟不变片段。这些结果迫切需要非经典方法来研究非初等类的双模拟和一阶表达性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bisimulation in Inquisitive Modal Logic
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, and characterise inquisitive modal logic as the bisimulation invariant fragments of first-order logic over various classes of two-sorted relational structures. These results crucially require non-classical methods in studying bisimulations and first-order expressiveness over non-elementary classes.
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