{"title":"一种实用的命题动态逻辑决策方法(初步报告)","authors":"V. Pratt","doi":"10.1145/800133.804362","DOIUrl":null,"url":null,"abstract":"We give a new characterization of the set of satisfiable formulae of propositional dynamic logic (PDL) based on the method of tableaux. From it we derive a heuristically efficient goal-directed proof procedure and a complete axiom system for PDL. The proof procedure illustrates a striking connection between natural deduction and symbolic execution. The completeness proof for the axiom system incorporates a method for the automatic synthesis of invariants. We also augment DL with new modalities throughout, during, and preserves, supply a new semantic foundation for DL programs, and show how to extend the satisfiability characterizations for PDL to throughout.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"117","resultStr":"{\"title\":\"A practical decision method for propositional dynamic logic (Preliminary Report)\",\"authors\":\"V. Pratt\",\"doi\":\"10.1145/800133.804362\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a new characterization of the set of satisfiable formulae of propositional dynamic logic (PDL) based on the method of tableaux. From it we derive a heuristically efficient goal-directed proof procedure and a complete axiom system for PDL. The proof procedure illustrates a striking connection between natural deduction and symbolic execution. The completeness proof for the axiom system incorporates a method for the automatic synthesis of invariants. We also augment DL with new modalities throughout, during, and preserves, supply a new semantic foundation for DL programs, and show how to extend the satisfiability characterizations for PDL to throughout.\",\"PeriodicalId\":313820,\"journal\":{\"name\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"117\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800133.804362\",\"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 of the tenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800133.804362","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A practical decision method for propositional dynamic logic (Preliminary Report)
We give a new characterization of the set of satisfiable formulae of propositional dynamic logic (PDL) based on the method of tableaux. From it we derive a heuristically efficient goal-directed proof procedure and a complete axiom system for PDL. The proof procedure illustrates a striking connection between natural deduction and symbolic execution. The completeness proof for the axiom system incorporates a method for the automatic synthesis of invariants. We also augment DL with new modalities throughout, during, and preserves, supply a new semantic foundation for DL programs, and show how to extend the satisfiability characterizations for PDL to throughout.