{"title":"The LindstrØm-Type Characterization of Hajek's Fuzzy Logic of Integrals","authors":"K. Jobczyk","doi":"10.1109/FUZZ45933.2021.9494394","DOIUrl":null,"url":null,"abstract":"In 1969, Per LindstrØm proved his famous theorem and established criteria for the first-order definability of formal theories for discrete structures. The results were extrapolated for systems of modal logic and even for theories for continuous structures. This paper aims to formulate and prove LindstrØm's theorem for analytic structures based on measures. In particular, Hajek's Logic of Integral is redefined as an abstract logic with a new type of Hajek's satisfiability and considered as a minimal logic in the class of analytic structures with Lebesgue integrals.","PeriodicalId":151289,"journal":{"name":"2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","volume":"107 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FUZZ45933.2021.9494394","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
In 1969, Per LindstrØm proved his famous theorem and established criteria for the first-order definability of formal theories for discrete structures. The results were extrapolated for systems of modal logic and even for theories for continuous structures. This paper aims to formulate and prove LindstrØm's theorem for analytic structures based on measures. In particular, Hajek's Logic of Integral is redefined as an abstract logic with a new type of Hajek's satisfiability and considered as a minimal logic in the class of analytic structures with Lebesgue integrals.
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