论文标题

好奇的逻辑是知道如何的认识论逻辑

Inquisitive Logic as an Epistemic Logic of Knowing How

论文作者

Wang, Haoyu, Wang, Yanjing, Wang, Yunsong

论文摘要

在本文中,我们提出了一种对命题好奇逻辑的替代解释,作为知道如何的认知逻辑。在我们的环境中,国家支持的好奇逻辑公式$α$被形式化为“知道如何解决$α$”(更通话,“知道$α$是true”)在与国家相对应的S5认知模型上。基于这种认知解释,我们使用动态的认识论逻辑,并与知识和知识符合操作员,以捕获构成逻辑中无辜的连接词背后的认知信息。我们表明,有效的知识公式集完全对应于好奇的逻辑。主要的结果是使用完整的动态认知语言进行完整的公理化完整的公理化。此外,我们表明,可以消除专有操作员和动态运算符,而不会改变模型的表达性,这与文献中存在的好奇逻辑的模态翻译一致。我们希望我们的框架可以在好奇逻辑中对各种概念和技术结果提供直观的替代解释,并提供一个强大而灵活的工具,可以在认知的背景下进行好奇的推理。

In this paper, we present an alternative interpretation of propositional inquisitive logic as an epistemic logic of knowing how. In our setting, an inquisitive logic formula $α$ being supported by a state is formalized as "knowing how to resolve $α$" (more colloquially, "knowing how $α$ is true") holds on the S5 epistemic model corresponding to the state. Based on this epistemic interpretation, we use a dynamic epistemic logic with both know-how and know-that operators to capture the epistemic information behind the innocent-looking connectives in inquisitive logic. We show that the set of valid know-how formulas corresponds precisely to the inquisitive logic. The main result is a complete axiomatization with intuitive axioms using the full dynamic epistemic language. Moreover, we show that the know-how operator and the dynamic operator can both be eliminated without changing the expressivity over models, which is consistent with the modal translation of inquisitive logic existing in the literature. We hope our framework can give an intuitive alternative interpretation of various concepts and technical results in inquisitive logic, and also provide a powerful and flexible tool to do inquisitive reasoning in an epistemic context.

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