扩展框架和逻辑原则的分离

M. Fujiwara, H. Ishihara, Takako Nemoto, Nobu-Yuki Suzuki, K. Yokoyama
{"title":"扩展框架和逻辑原则的分离","authors":"M. Fujiwara, H. Ishihara, Takako Nemoto, Nobu-Yuki Suzuki, K. Yokoyama","doi":"10.1017/bsl.2023.29","DOIUrl":null,"url":null,"abstract":"Abstract We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic \n$\\mathbf {IQC}$\n and first-order arithmetic \n$\\mathbf {HA}$\n from a Kripke model for intuitionistic propositional logic \n$\\mathbf {IPC}$\n . 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 \n$\\mathbf {IQC}$\n and a separation theorem of a sentence from a set of schemata in \n$\\mathbf {HA}$\n . We see several examples which give us separations among omniscience principles.","PeriodicalId":22265,"journal":{"name":"The Bulletin of Symbolic Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES\",\"authors\":\"M. Fujiwara, H. Ishihara, Takako Nemoto, Nobu-Yuki Suzuki, K. Yokoyama\",\"doi\":\"10.1017/bsl.2023.29\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic \\n$\\\\mathbf {IQC}$\\n and first-order arithmetic \\n$\\\\mathbf {HA}$\\n from a Kripke model for intuitionistic propositional logic \\n$\\\\mathbf {IPC}$\\n . 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 \\n$\\\\mathbf {IQC}$\\n and a separation theorem of a sentence from a set of schemata in \\n$\\\\mathbf {HA}$\\n . We see several examples which give us separations among omniscience principles.\",\"PeriodicalId\":22265,\"journal\":{\"name\":\"The Bulletin of Symbolic Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Bulletin of Symbolic Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/bsl.2023.29\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Bulletin of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/bsl.2023.29","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信