{"title":"没有语义的微积分理论的连续体","authors":"A. Salibra","doi":"10.1109/LICS.2001.932509","DOIUrl":null,"url":null,"abstract":"In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.","PeriodicalId":366313,"journal":{"name":"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science","volume":"279 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"22","resultStr":"{\"title\":\"A continuum of theories of lambda calculus without semantics\",\"authors\":\"A. Salibra\",\"doi\":\"10.1109/LICS.2001.932509\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.\",\"PeriodicalId\":366313,\"journal\":{\"name\":\"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science\",\"volume\":\"279 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 16th Annual IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2001.932509\",\"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 16th Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2001.932509","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A continuum of theories of lambda calculus without semantics
In this paper, we give a topological proof of the following result: there exist 2¿(/spl aleph//sub 0/) lambda theories of the untyped lambda calculus without a model in any semantics based on D.S. Scott's (1972, 1981) view of models as partially ordered sets and of functions as monotonic functions. As a consequence of this result, we positively solve the conjecture, stated by O. Bastonero and X. Gouy (1999) and by C. Berline (2000), that the strongly stable semantics is incomplete.
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