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Epistemic extensions of substructural inquisitive logics

机译:子结构好奇逻辑的认知扩展

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In this paper, we study the epistemic extensions of distributive substructural inquisitive logics. Substructural inquisitive logics are logics of questions based on substructural logics of declarative sentences. They generalize basic inquisitive logic which is based on the classical logic of declaratives. We show that if the underlying substructural logic is distributive, the generalization can be extended to embrace also the epistemic modalities 'knowing whether' and 'wondering whether' that are applicable to questions. We construct a semantic framework for a language of propositional substructural logics enriched with a question-forming operator (inquisitive disjunction) and epistemic modalities. We show that within this framework, one can define a canonical model with suitable properties for any (syntactically defined) epistemic inquisitive logic. This leads to a general approach to completeness proofs for such logics. A deductive system for the weakest epistemic inquisitive logic is described and completeness proved for this special case using the general method.
机译:在本文中,我们研究了分配子结构好奇逻辑的认知延伸。子结构好奇逻辑是基于声明性句子的子结构逻辑的问题逻辑。他们概括了基本的好奇逻辑,该逻辑是基于古典宣言的逻辑。我们表明,如果潜在的子结构逻辑是分配的,则可以扩展到延伸以接受认识的方式“了解'是否”想知道这是适用的问题。我们构建了一种语义的语言,用于提出富有问题的操作员(好奇分离)和认知方式的命题子结构逻辑语言。我们在此框架内显示,可以为任何(句法定义)认真正明逻辑定义具有适当属性的规范模型。这导致了这种逻辑的完整性证明的一般方法。描述了最弱的认识性好奇逻辑的演绎系统,并使用一般方法证明了这种特殊情况的完整性。

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