{"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":"<p>We introduce a single-set axiomatisation of cubical <span>\\(\\omega \\)</span>-categories, including connections and inverses. We justify these axioms by establishing a series of equivalences between the category of single-set cubical <span>\\(\\omega \\)</span>-categories, and their variants with connections and inverses, and the corresponding cubical <span>\\(\\omega \\)</span>-categories. We also report on the formalisation of cubical <span>\\(\\omega \\)</span>-categories with the Isabelle/HOL proof assistant, which has been instrumental in developing the single-set axiomatisation.</p>","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}
引用次数: 0
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
