{"title":"A Modification of Visser’s Formal Logic and Its Connection with Solovay’s Modal Logic","authors":"","doi":"10.3103/s1066369x23110051","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p>We present a new logic called <strong>SPL</strong>, embedded into Solovay’s provability logic <strong>S</strong>, using a translation that embeds Visser’s formal logic <strong>FPL</strong> into Gödel–Löb’s provability logic <strong>GL</strong>. <strong>SPL</strong> is formulated as sequent and natural deduction calculi, and a the Kripke semantics is proposed for <strong>SPL</strong>.</p> </span>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x23110051","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We present a new logic called SPL, embedded into Solovay’s provability logic S, using a translation that embeds Visser’s formal logic FPL into Gödel–Löb’s provability logic GL. SPL is formulated as sequent and natural deduction calculi, and a the Kripke semantics is proposed for SPL.
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