{"title":"New New Modification of the Subformula Property for a Modal Logic","authors":"M. Takano","doi":"10.18778/0138-0680.2020.15","DOIUrl":null,"url":null,"abstract":"A modified subformula property for the modal logic KD with the additional axiom \n$\\Box\\Diamond(A\\vee B)\\supset\\Box\\Diamond A\\vee\\Box\\Diamond B$ is shown. \nA new modification of the notion of subformula is proposed for this purpose. \nThis modification forms a natural extension of our former one \non which modified subformula property for the modal logics K5, K5D and S4.2 has been shown \n(Bull Sect Logic 30:115--122, 2001 and 48:19--28, 2019). \nThe finite model property as well as decidability for the logic follows from this.","PeriodicalId":38667,"journal":{"name":"Bulletin of the Section of Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Section of Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/0138-0680.2020.15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 2
Abstract
A modified subformula property for the modal logic KD with the additional axiom
$\Box\Diamond(A\vee B)\supset\Box\Diamond A\vee\Box\Diamond B$ is shown.
A new modification of the notion of subformula is proposed for this purpose.
This modification forms a natural extension of our former one
on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown
(Bull Sect Logic 30:115--122, 2001 and 48:19--28, 2019).
The finite model property as well as decidability for the logic follows from this.
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