{"title":"基于方案的自然数系统探索","authors":"Madalina Hodorog, A. Craciun","doi":"10.1109/SYNASC.2006.67","DOIUrl":null,"url":null,"abstract":"In this paper, we report a case study of computer supported exploration of the theory of natural numbers, using a theory exploration model based on knowledge schemes, proposed by Bruno Buchberger. We illustrate with examples from the exploration: (i) the invention of new concepts (functions, relations) in the theory, using knowledge scheme;, (ii) the invention of new propositions, using proposition schemes; (iii) the invention of problems, using knowledge schemes; (iv) the introduction of new reasoning rules, by lifting knowledge to the inference level, after their correctness was proved","PeriodicalId":309740,"journal":{"name":"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Scheme-Based Systematic Exploration of Natural Numbers\",\"authors\":\"Madalina Hodorog, A. Craciun\",\"doi\":\"10.1109/SYNASC.2006.67\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we report a case study of computer supported exploration of the theory of natural numbers, using a theory exploration model based on knowledge schemes, proposed by Bruno Buchberger. We illustrate with examples from the exploration: (i) the invention of new concepts (functions, relations) in the theory, using knowledge scheme;, (ii) the invention of new propositions, using proposition schemes; (iii) the invention of problems, using knowledge schemes; (iv) the introduction of new reasoning rules, by lifting knowledge to the inference level, after their correctness was proved\",\"PeriodicalId\":309740,\"journal\":{\"name\":\"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SYNASC.2006.67\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2006.67","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Scheme-Based Systematic Exploration of Natural Numbers
In this paper, we report a case study of computer supported exploration of the theory of natural numbers, using a theory exploration model based on knowledge schemes, proposed by Bruno Buchberger. We illustrate with examples from the exploration: (i) the invention of new concepts (functions, relations) in the theory, using knowledge scheme;, (ii) the invention of new propositions, using proposition schemes; (iii) the invention of problems, using knowledge schemes; (iv) the introduction of new reasoning rules, by lifting knowledge to the inference level, after their correctness was proved
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