通过语言,从类型空间到概率框架再回来

Adam Bjorndahl, Joseph Y. Halpern
{"title":"通过语言,从类型空间到概率框架再回来","authors":"Adam Bjorndahl, Joseph Y. Halpern","doi":"10.4204/EPTCS.251.6","DOIUrl":null,"url":null,"abstract":"We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this \"language parameter\" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"From Type Spaces to Probability Frames and Back, via Language\",\"authors\":\"Adam Bjorndahl, Joseph Y. Halpern\",\"doi\":\"10.4204/EPTCS.251.6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this \\\"language parameter\\\" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.\",\"PeriodicalId\":118894,\"journal\":{\"name\":\"Theoretical Aspects of Rationality and Knowledge\",\"volume\":\"31 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Aspects of Rationality and Knowledge\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/EPTCS.251.6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Aspects of Rationality and Knowledge","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.251.6","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

我们研究了交互信念建模的两个主要数学框架:Harsanyi类型空间和可能世界风格概率框架之间的联系。虽然将前者翻译成后者很简单,但我们证明了反向翻译隐含地依赖于背景逻辑语言。一旦明确了这个“语言参数”,它就揭示了通用类型空间和规范模型之间的密切关系:也就是说,它们本质上是相同的结构。由于规范模型的性质在很大程度上取决于用于生成它的背景逻辑,这项工作为通用类型空间的相应景观提供了一种新的视角。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
From Type Spaces to Probability Frames and Back, via Language
We investigate the connection between the two major mathematical frameworks for modeling interactive beliefs: Harsanyi type spaces and possible-worlds style probability frames. While translating the former into the latter is straightforward, we demonstrate that the reverse translation relies implicitly on a background logical language. Once this "language parameter" is made explicit, it reveals a close relationship between universal type spaces and canonical models: namely, that they are essentially the same construct. As the nature of a canonical model depends heavily on the background logic used to generate it, this work suggests a new view into a corresponding landscape of universal type spaces.
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
期刊最新文献
Strengthening Consistency Results in Modal Logic A Logic-Based Analysis of Responsibility Epistemic Logics of Structured Intensional Groups Complete Conditional Type Structures (Extended Abstract) Selling Data to a Competitor
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1