{"title":"Compact propositional Godel logics","authors":"M. Baaz, R. Zach","doi":"10.1109/ISMVL.1998.679315","DOIUrl":null,"url":null,"abstract":"Entailment in propositional Godel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Godel logics, only one of which is compact. It is also shown that the compact infinite-valued Godel logic is the only one which interpolates, and the only one with an r.e. entailment relation.","PeriodicalId":377860,"journal":{"name":"Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"44","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.1998.679315","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 44
Abstract
Entailment in propositional Godel logics can be defined in a natural way. While all infinite sets of truth values yield the same sets of tautologies, the entailment relations differ. It is shown that there is a rich structure of infinite-valued Godel logics, only one of which is compact. It is also shown that the compact infinite-valued Godel logic is the only one which interpolates, and the only one with an r.e. entailment relation.
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