{"title":"论关联逻辑的表前扩展","authors":"Asadollah Fallahi, James Gordon Raftery","doi":"10.1007/s11225-023-10081-2","DOIUrl":null,"url":null,"abstract":"<p>We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom <span>\\((p\\rightarrow q)\\vee (q\\rightarrow p)\\)</span> has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Pretabular Extensions of Relevance Logic\",\"authors\":\"Asadollah Fallahi, James Gordon Raftery\",\"doi\":\"10.1007/s11225-023-10081-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom <span>\\\\((p\\\\rightarrow q)\\\\vee (q\\\\rightarrow p)\\\\)</span> has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11225-023-10081-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11225-023-10081-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们展示了无限多的半线性De Morgan monoids(以及类似的相关代数)的半简单变种，它们不是表列的，而是只有表列的固有子变种。因此，无论阿克曼常数是否存在，公理\((p\rightarrow q)\vee (q\rightarrow p)\)对关联逻辑的扩展都具有无限多的表前公理扩展。
We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom \((p\rightarrow q)\vee (q\rightarrow p)\) has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.
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