{"title":"确定实值函数的谓词逻辑理论","authors":"Stefan Ratschan","doi":"10.48550/arXiv.2306.16505","DOIUrl":null,"url":null,"abstract":"The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Deciding Predicate Logical Theories of Real-Valued Functions\",\"authors\":\"Stefan Ratschan\",\"doi\":\"10.48550/arXiv.2306.16505\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.\",\"PeriodicalId\":369104,\"journal\":{\"name\":\"International Symposium on Mathematical Foundations of Computer Science\",\"volume\":\"25 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Mathematical Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2306.16505\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Mathematical Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2306.16505","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Deciding Predicate Logical Theories of Real-Valued Functions
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.
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