{"title":"偏微分的完全等式公理化","authors":"Gordon D. Plotkin","doi":"10.1016/j.entcs.2020.09.011","DOIUrl":null,"url":null,"abstract":"<div><p>We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi's interpolation theorem that all multivariate Hermite problems are solvable. We also present a number of related results, such as decidability and equational completeness.</p></div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2020.09.011","citationCount":"1","resultStr":"{\"title\":\"A Complete Equational Axiomatisation of Partial Differentiation\",\"authors\":\"Gordon D. Plotkin\",\"doi\":\"10.1016/j.entcs.2020.09.011\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi's interpolation theorem that all multivariate Hermite problems are solvable. We also present a number of related results, such as decidability and equational completeness.</p></div>\",\"PeriodicalId\":38770,\"journal\":{\"name\":\"Electronic Notes in Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.entcs.2020.09.011\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571066120300621\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571066120300621","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}
A Complete Equational Axiomatisation of Partial Differentiation
We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi's interpolation theorem that all multivariate Hermite problems are solvable. We also present a number of related results, such as decidability and equational completeness.
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