Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic

Pub Date : 2024-03-06 DOI:10.1007/s11225-024-10095-4

引用次数: 0

Abstract

Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property of some quasi-Boolean modal logics is proved. A cut-free Gentzen sequent calculus for the minimal quasi-Boolean logic is developed and we show that it has the Craig interpolation property.

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准布尔模态逻辑的克里普克完备性和序列微积分

摘要准布尔模态逻辑是具有满足交互公理的模态算子的准布尔模态逻辑。介绍了顺序准布尔模态逻辑和关系语义。用典型模型法证明了一些准布尔模态逻辑的克里普克完备性。我们证明了每一个描述性持久准布尔模态逻辑都是典型的。证明了一些准布尔模态逻辑的有限模型性质。我们为最小准布尔逻辑建立了一个无切割的根岑序列微积分，并证明它具有克雷格插值特性。

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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