{"title":"Combining Higher-Order Logic with Set Theory Formalizations.","authors":"Cezary Kaliszyk, Karol Pąk","doi":"10.1007/s10817-023-09663-5","DOIUrl":null,"url":null,"abstract":"<p><p>The Isabelle Higher-order Tarski-Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we align significant parts of these two libraries, by defining isomorphisms between their concepts, including the real numbers and algebraic structures. The isomorphisms allow us to transport theorems between the foundations and use the results from the libraries simultaneously.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"67 2","pages":"20"},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10209288/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Automated Reasoning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10817-023-09663-5","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/5/25 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
The Isabelle Higher-order Tarski-Grothendieck object logic includes in its foundations both higher-order logic and set theory, which allows importing the libraries of Isabelle/HOL and Isabelle/Mizar. The two libraries, however, define all the basic concepts independently, which means that the results in the two are disconnected. In this paper, we align significant parts of these two libraries, by defining isomorphisms between their concepts, including the real numbers and algebraic structures. The isomorphisms allow us to transport theorems between the foundations and use the results from the libraries simultaneously.
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.
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