单集立方范畴及其形式化与证明助手

IF 0.9 3区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Journal of Automated Reasoning Pub Date : 2024-09-12 DOI:10.1007/s10817-024-09710-9

Philippe Malbos, Tanguy Massacrier, Georg Struth

{"title":"单集立方范畴及其形式化与证明助手","authors":"Philippe Malbos, Tanguy Massacrier, Georg Struth","doi":"10.1007/s10817-024-09710-9","DOIUrl":null,"url":null,"abstract":"We introduce a single-set axiomatisation of cubical \\(\\omega \\)-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical \\(\\omega \\)-categories, and their variants with connections and inverses, and the corresponding cubical \\(\\omega \\)-categories. We also report on the formalisation of cubical \\(\\omega \\)-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"76 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Single-Set Cubical Categories and Their Formalisation with a Proof Assistant\",\"authors\":\"Philippe Malbos, Tanguy Massacrier, Georg Struth\",\"doi\":\"10.1007/s10817-024-09710-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a single-set axiomatisation of cubical \\\\(\\\\omega \\\\)-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical \\\\(\\\\omega \\\\)-categories, and their variants with connections and inverses, and the corresponding cubical \\\\(\\\\omega \\\\)-categories. We also report on the formalisation of cubical \\\\(\\\\omega \\\\)-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.\",\"PeriodicalId\":15082,\"journal\":{\"name\":\"Journal of Automated Reasoning\",\"volume\":\"76 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-09-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Automated Reasoning\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s10817-024-09710-9\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Automated Reasoning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10817-024-09710-9","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了立方（\omega \）范畴的单集公理化，包括连接和逆。我们通过在单集立方（\omega \）范畴及其包含连接和反转的变体与相应的立方（\omega \）范畴之间建立一系列等价关系来证明这些公理。我们还报告了用 Isabelle/HOL 证明助手对立方（\omega \）-类的形式化，它在发展单集公理化方面发挥了重要作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Single-Set Cubical Categories and Their Formalisation with a Proof Assistant

We introduce a single-set axiomatisation of cubical \(\omega \)-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical \(\omega \)-categories, and their variants with connections and inverses, and the corresponding cubical \(\omega \)-categories. We also report on the formalisation of cubical \(\omega \)-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.

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

Journal of Automated Reasoning 工程技术-计算机：人工智能

CiteScore

3.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning. The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.