{"title":"整数和实数上可定一阶逻辑的分解","authors":"F. Bouchy, A. Finkel, Jérôme Leroux","doi":"10.1109/TIME.2008.22","DOIUrl":null,"url":null,"abstract":"We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation.","PeriodicalId":142549,"journal":{"name":"2008 15th International Symposium on Temporal Representation and Reasoning","volume":"41 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Decomposition of Decidable First-Order Logics over Integers and Reals\",\"authors\":\"F. Bouchy, A. Finkel, Jérôme Leroux\",\"doi\":\"10.1109/TIME.2008.22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation.\",\"PeriodicalId\":142549,\"journal\":{\"name\":\"2008 15th International Symposium on Temporal Representation and Reasoning\",\"volume\":\"41 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 15th International Symposium on Temporal Representation and Reasoning\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/TIME.2008.22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 15th International Symposium on Temporal Representation and Reasoning","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TIME.2008.22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Decomposition of Decidable First-Order Logics over Integers and Reals
We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation.
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