ALGEBRAIC SEMANTICS FOR RELATIVE TRUTH, AWARENESS, AND POSSIBILITY

IF 0.9 3区数学 Q1 LOGIC

Review of Symbolic Logic Pub Date : 2023-09-28 DOI:10.1017/s1755020323000308

Evan Piermont

引用次数: 0

Abstract

Abstract This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators—akin to the theory of modal Algebras—RBAs serve as models of modal logics in which truth is relative. In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics.

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相对真、觉知和可能性的代数语义

摘要本文提出了一类代数结构——相对布尔代数(RBAs)，它为命题逻辑提供了语义，其中真值/有效性仅相对于局部域定义。特别是，事件及其补充的连接不必是顶部元素。尽管如此，行为是由命题逻辑法则局部支配的。通过进一步赋予这些结构算子——类似于模态代数理论——rba充当了真理是相对的模态逻辑的模型。特别是，模态rba为各种已知的感知逻辑和可能性语义的另一种视图提供语义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Review of Symbolic Logic 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Review of Symbolic Logic is designed to cultivate research on the borders of logic, philosophy, and the sciences, and to support substantive interactions between these disciplines. The journal welcomes submissions in any of the following areas, broadly construed: - The general study of logical systems and their semantics,including non-classical logics and algebraic logic; - Philosophical logic and formal epistemology, including interactions with decision theory and game theory; - The history, philosophy, and methodology of logic and mathematics, including the history of philosophy of logic and mathematics; - Applications of logic to the sciences, such as computer science, cognitive science, and linguistics; and logical results addressing foundational issues in the sciences.