{"title":"Coq中二阶逻辑的不可判定性、不完备性和完备性","authors":"Mark Koch, Dominik Kirst","doi":"10.1145/3497775.3503684","DOIUrl":null,"url":null,"abstract":"We mechanise central metatheoretic results about second-order logic (SOL) using the Coq proof assistant. Concretely, we consider undecidability via many-one reduction from Diophantine equations (Hilbert's tenth problem), incompleteness regarding full semantics via categoricity of second-order Peano arithmetic, and completeness regarding Henkin semantics via translation to mono-sorted first-order logic (FOL). Moreover, this translation is used to transport further characteristic properties of FOL to SOL, namely the compactness and Löwenheim-Skolem theorems.","PeriodicalId":196529,"journal":{"name":"Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Undecidability, incompleteness, and completeness of second-order logic in Coq\",\"authors\":\"Mark Koch, Dominik Kirst\",\"doi\":\"10.1145/3497775.3503684\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We mechanise central metatheoretic results about second-order logic (SOL) using the Coq proof assistant. Concretely, we consider undecidability via many-one reduction from Diophantine equations (Hilbert's tenth problem), incompleteness regarding full semantics via categoricity of second-order Peano arithmetic, and completeness regarding Henkin semantics via translation to mono-sorted first-order logic (FOL). Moreover, this translation is used to transport further characteristic properties of FOL to SOL, namely the compactness and Löwenheim-Skolem theorems.\",\"PeriodicalId\":196529,\"journal\":{\"name\":\"Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-01-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3497775.3503684\",\"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 of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3497775.3503684","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Undecidability, incompleteness, and completeness of second-order logic in Coq
We mechanise central metatheoretic results about second-order logic (SOL) using the Coq proof assistant. Concretely, we consider undecidability via many-one reduction from Diophantine equations (Hilbert's tenth problem), incompleteness regarding full semantics via categoricity of second-order Peano arithmetic, and completeness regarding Henkin semantics via translation to mono-sorted first-order logic (FOL). Moreover, this translation is used to transport further characteristic properties of FOL to SOL, namely the compactness and Löwenheim-Skolem theorems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
