量词深度为 4 的 FO 逻辑谱是有限的

IF 0.7 4区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Computational Logic Pub Date : 2024-01-22 DOI:10.1145/3641547

Yury Yarovikov, Maksim Zhukovskii

{"title":"量词深度为 4 的 FO 逻辑谱是有限的","authors":"Yury Yarovikov, Maksim Zhukovskii","doi":"10.1145/3641547","DOIUrl":null,"url":null,"abstract":"The k-spectrum is the set of all α > 0 such that G(n, n− α) does not obey the 0-1 law for FO sentences with quantifier depth at most k. In this paper, we prove that the minimum k such that the k-spectrum is infinite equals 5.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"256 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spectrum of FO Logic With Quantifier Depth 4 Is Finite\",\"authors\":\"Yury Yarovikov, Maksim Zhukovskii\",\"doi\":\"10.1145/3641547\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The k-spectrum is the set of all α > 0 such that G(n, n− α) does not obey the 0-1 law for FO sentences with quantifier depth at most k. In this paper, we prove that the minimum k such that the k-spectrum is infinite equals 5.\",\"PeriodicalId\":50916,\"journal\":{\"name\":\"ACM Transactions on Computational Logic\",\"volume\":\"256 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Transactions on Computational Logic\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1145/3641547\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computational Logic","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1145/3641547","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

k 谱是所有 α > 0 的集合，对于量词深度最多为 k 的 FO 句子，G(n, n- α) 不遵守 0-1 规律。在本文中，我们证明了使 k 谱无限大的最小 k 等于 5。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Spectrum of FO Logic With Quantifier Depth 4 Is Finite

The k-spectrum is the set of all α > 0 such that G(n, n^{− α}) does not obey the 0-1 law for FO sentences with quantifier depth at most k. In this paper, we prove that the minimum k such that the k-spectrum is infinite equals 5.

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

ACM Transactions on Computational Logic 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. This area has a great tradition in computer science. Several researchers who earned the ACM Turing award have also contributed to this field, namely Edgar Codd (relational database systems), Stephen Cook (complexity of logical theories), Edsger W. Dijkstra, Robert W. Floyd, Tony Hoare, Amir Pnueli, Dana Scott, Edmond M. Clarke, Allen E. Emerson, and Joseph Sifakis (program logics, program derivation and verification, programming languages semantics), Robin Milner (interactive theorem proving, concurrency calculi, and functional programming), and John McCarthy (functional programming and logics in AI). Logic continues to play an important role in computer science and has permeated several of its areas, including artificial intelligence, computational complexity, database systems, and programming languages. The Editorial Board of this journal seeks and hopes to attract high-quality submissions in all the above-mentioned areas of computational logic so that TOCL becomes the standard reference in the field. Both theoretical and applied papers are sought. Submissions showing novel use of logic in computer science are especially welcome.

期刊最新文献

Fundamental Logic is Decidable Strong Backdoors for Default Logic One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus Stackelberg-Pareto Synthesis First-Order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications