{"title":"The Topology-Free Construction of the Universal Type Structure for Conditional Probability Systems","authors":"Pierfrancesco Guarino","doi":"10.4204/EPTCS.251.20","DOIUrl":null,"url":null,"abstract":"We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Aspects of Rationality and Knowledge","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.251.20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.
我们构造了不带拓扑假设的条件概率系统的普适型结构，即一种终端型、信念完备型和非冗余型结构。特别地，为了以建设性的方式获得相信完备性，我们推广了Meier [a∞Probability Logic for Type Spaces]的工作。数学学报，1999,19 (1):1- 8 [j] .用数学方法证明了具有真实和非认知条件事件的无限概率逻辑的强完备性。
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