范畴概率中的扩张和信息流公理

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2023-10-25 DOI:10.1017/s0960129523000324

Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Antonio Lorenzin, Paolo Perrone, Dario Stein

{"title":"范畴概率中的扩张和信息流公理","authors":"Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Antonio Lorenzin, Paolo Perrone, Dario Stein","doi":"10.1017/s0960129523000324","DOIUrl":null,"url":null,"abstract":"Abstract We study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity , but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"58 5","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Dilations and information flow axioms in categorical probability\",\"authors\":\"Tobias Fritz, Tomáš Gonda, Nicholas Gauguin Houghton-Larsen, Antonio Lorenzin, Paolo Perrone, Dario Stein\",\"doi\":\"10.1017/s0960129523000324\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity , but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation.\",\"PeriodicalId\":49855,\"journal\":{\"name\":\"Mathematical Structures in Computer Science\",\"volume\":\"58 5\",\"pages\":\"0\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Structures in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/s0960129523000324\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Structures in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0960129523000324","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 6

摘要

摘要研究了马尔可夫范畴的正性和因果性公理作为膨胀和信息流的性质，并给出了任意半笛卡尔一元范畴的正性和因果性公理的变化。这些帮助我们证明了正马尔可夫范畴仅仅是对称一元范畴的附加性质(而不是额外的结构)。我们还描述了可表征马尔可夫范畴的正性，并证明因果关系意味着正性，而不是相反。最后，我们注意到准borel空间的正性失败，并将这种失败解释为概率名称生成的隐私属性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Dilations and information flow axioms in categorical probability

Abstract We study the positivity and causality axioms for Markov categories as properties of dilations and information flow and also develop variations thereof for arbitrary semicartesian monoidal categories. These help us show that being a positive Markov category is merely an additional property of a symmetric monoidal category (rather than extra structure). We also characterize the positivity of representable Markov categories and prove that causality implies positivity , but not conversely. Finally, we note that positivity fails for quasi-Borel spaces and interpret this failure as a privacy property of probabilistic name generation.

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

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.