{"title":"多值概率论","authors":"C. Morgan","doi":"10.1109/ISMVL.2004.1319958","DOIUrl":null,"url":null,"abstract":"The apparent conflict between many valued logic and probability theory is resolved if we treat the probability of a sentence as the probability that the sentence has some specified truth value. The classical probability of a sentence is the probability that the sentence is classically true. In an analogous way, we develop a class of probability theories appropriate for any finite valued logics; the probability of a sentence is interpreted as the probability that the sentence takes some value in a specified subset of the semantic range. We show that for any finite valued logic, there is an appropriate many valued probability theory providing a characteristic probabilistic semantics for which the logic is both sound and complete.","PeriodicalId":285497,"journal":{"name":"Proceedings. 34th International Symposium on Multiple-Valued Logic","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Many valued probability theory\",\"authors\":\"C. Morgan\",\"doi\":\"10.1109/ISMVL.2004.1319958\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The apparent conflict between many valued logic and probability theory is resolved if we treat the probability of a sentence as the probability that the sentence has some specified truth value. The classical probability of a sentence is the probability that the sentence is classically true. In an analogous way, we develop a class of probability theories appropriate for any finite valued logics; the probability of a sentence is interpreted as the probability that the sentence takes some value in a specified subset of the semantic range. We show that for any finite valued logic, there is an appropriate many valued probability theory providing a characteristic probabilistic semantics for which the logic is both sound and complete.\",\"PeriodicalId\":285497,\"journal\":{\"name\":\"Proceedings. 34th International Symposium on Multiple-Valued Logic\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. 34th International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2004.1319958\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 34th International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2004.1319958","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The apparent conflict between many valued logic and probability theory is resolved if we treat the probability of a sentence as the probability that the sentence has some specified truth value. The classical probability of a sentence is the probability that the sentence is classically true. In an analogous way, we develop a class of probability theories appropriate for any finite valued logics; the probability of a sentence is interpreted as the probability that the sentence takes some value in a specified subset of the semantic range. We show that for any finite valued logic, there is an appropriate many valued probability theory providing a characteristic probabilistic semantics for which the logic is both sound and complete.
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