Common Knowledge in a Logic of Gossips

K. Apt, D. Wojtczak
{"title":"Common Knowledge in a Logic of Gossips","authors":"K. Apt, D. Wojtczak","doi":"10.4204/EPTCS.251.2","DOIUrl":null,"url":null,"abstract":"Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. \nWe study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). \nK. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Aspects of Rationality and Knowledge","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.251.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8

Abstract

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.
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
八卦逻辑中的常识
八卦协议旨在通过点对点或群体通信的方式,达到一种所有特工都知道彼此秘密的状态。最近,许多作者研究了分布式认知八卦协议。这些协议使用来自简单认知逻辑的保护公式,这使得它们的分析和验证更加容易。我们在这里研究这种逻辑背景下的常识。首先,我们分析了它何时可以被简化为迭代知识。然后证明了没有嵌套公共知识算子的公式的语义和真值是可判定的。这意味着使用非嵌套公共知识算子的分布式知识八卦协议的可实现性、部分正确性和终止性也是可确定的。鉴于共同知识等同于嵌套知识的无限结合,这些结果是对(Apt & Wojtczak, 2016)中建立的原始认知逻辑的相应可判定性结果的非平凡推广。K. R. Apt & D. Wojtczak(2016):论八卦逻辑的可决性。中国生物医学工程学报,2016,pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 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