{"title":"WCP 全球可接受推理规则的明确基础","authors":"V. V. Rimatskii","doi":"10.1007/s10469-024-09733-6","DOIUrl":null,"url":null,"abstract":"<p>Inference rules are examined which are admissible immediately in all residually finite extensions of <i>S</i>4 possessing the weak cocover property. An explicit basis is found for such <i>WCP</i>-globally admissible rules. In case of tabular logics, the basis is finite, and for residually finite extensions, the independency of an explicit basis is proved.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Explicit Basis for WCP-Globally Admissible Inference Rules\",\"authors\":\"V. V. Rimatskii\",\"doi\":\"10.1007/s10469-024-09733-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Inference rules are examined which are admissible immediately in all residually finite extensions of <i>S</i>4 possessing the weak cocover property. An explicit basis is found for such <i>WCP</i>-globally admissible rules. In case of tabular logics, the basis is finite, and for residually finite extensions, the independency of an explicit basis is proved.</p>\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10469-024-09733-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10469-024-09733-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
An Explicit Basis for WCP-Globally Admissible Inference Rules
Inference rules are examined which are admissible immediately in all residually finite extensions of S4 possessing the weak cocover property. An explicit basis is found for such WCP-globally admissible rules. In case of tabular logics, the basis is finite, and for residually finite extensions, the independency of an explicit basis is proved.
期刊介绍：
This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions.
Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
All articles are peer-reviewed.
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