模态逻辑的子公式性质的新的修正

Q2 Arts and Humanities Bulletin of the Section of Logic Pub Date : 2020-08-15 DOI:10.18778/0138-0680.2020.15

M. Takano

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引用次数: 2

摘要

给出了具有附加公理$\Box\DDiamond（A\vee B）\supset\Box\DDiamond A\vee\Box\DDiamondB$的模态逻辑KD的一个修改的子公式性质。为此，提出了对子形式概念的一种新的修改。这种修改形成了我们前一个修改的自然扩展，在前一个上已经显示了模态逻辑K5、K5D和S4.2的修改子形式性质（Bull Sect Logic 30:115-1222001和48:19-282019）。有限模型的性质以及逻辑的可判定性由此而来。

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New New Modification of the Subformula Property for a Modal Logic

A modified subformula property for the modal logic KD with the additional axiom $\Box\Diamond(A\vee B)\supset\Box\Diamond A\vee\Box\Diamond B$ is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown (Bull Sect Logic 30:115--122, 2001 and 48:19--28, 2019). The finite model property as well as decidability for the logic follows from this.

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