扩展框架和逻辑原则的分离

M. Fujiwara, H. Ishihara, Takako Nemoto, Nobu-Yuki Suzuki, K. Yokoyama
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引用次数: 2

摘要

摘要本文旨在从直觉命题逻辑的Kripke模型$\mathbf {IPC}$中构造直觉谓词逻辑$\mathbf {IQC}$和一阶算术$\mathbf {HA}$的Kripke模型,发展一种系统的分离全知原理的方法。为此,我们引入了扩展帧的概念,并证明了每个IPC-Kripke模型都会产生一个扩展帧。利用IPC-Kripke模型生成的扩展框架,给出了$\mathbf {IQC}$中一个模式与一组模式的分离定理,以及$\mathbf {HA}$中一个句子与一组模式的分离定理。我们看到几个例子,给我们在全知原则之间的分离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES
Abstract We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$ . To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$ . We see several examples which give us separations among omniscience principles.
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