{"title":"Rules of definitional reflection","authors":"P. Schroeder-Heister","doi":"10.1109/LICS.1993.287585","DOIUrl":null,"url":null,"abstract":"The author discusses two rules of definitional reflection: the logical version of definitional reflection, as used in the extended logic programming language GCLA, and the omega version of definitional reflection. The logical version is a left-introduction rule completely analogous to the left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the omega version extends the logical version by a principle related to the omega rule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":"4 1","pages":"222-232"},"PeriodicalIF":0.0000,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"124","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.1993.287585","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 124
Abstract
The author discusses two rules of definitional reflection: the logical version of definitional reflection, as used in the extended logic programming language GCLA, and the omega version of definitional reflection. The logical version is a left-introduction rule completely analogous to the left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the omega version extends the logical version by a principle related to the omega rule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection.<>
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
![[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science](/Content/css/sci/img/zetp.jpg)
求助内容：
应助结果提醒方式：
扫码关注我们
