Separation logic is an extension of Hoare logic for reasoning about mutable heap structure. To represent separation logic in the first-order logic, there are several choices to determine what are constants, what are predicates and quantifiers, and whether the commands are taken as atomic or composite. This paper shall give a translation of separation logic into a guarded fragment of the first-order logic, such that the translation is faithful, that is, the translation translates a consistent statement (boolean expression, assertion or specification) of separation logic into a consistent formula in the fragment of the first-order logic. By the decidability of the satisfiability problem of the guarded first-order logic, if the commands are taken as atomic in the first-order logic then the guarded first-order logic translated from separation logic is decidable, if the commands are taken as atomic/composite in the first-order logic then the first-order logic translated from separation logic is undecidable.
{"title":"Translating Separation Logic into a Fragment of the First-Order Logic","authors":"Yuefei Sui, Yuming Shen, C. Cao, Ju Wang","doi":"10.1109/SKG.2010.29","DOIUrl":"https://doi.org/10.1109/SKG.2010.29","url":null,"abstract":"Separation logic is an extension of Hoare logic for reasoning about mutable heap structure. To represent separation logic in the first-order logic, there are several choices to determine what are constants, what are predicates and quantifiers, and whether the commands are taken as atomic or composite. This paper shall give a translation of separation logic into a guarded fragment of the first-order logic, such that the translation is faithful, that is, the translation translates a consistent statement (boolean expression, assertion or specification) of separation logic into a consistent formula in the fragment of the first-order logic. By the decidability of the satisfiability problem of the guarded first-order logic, if the commands are taken as atomic in the first-order logic then the guarded first-order logic translated from separation logic is decidable, if the commands are taken as atomic/composite in the first-order logic then the first-order logic translated from separation logic is undecidable.","PeriodicalId":105513,"journal":{"name":"2010 Sixth International Conference on Semantics, Knowledge and Grids","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127337059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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