{"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}
引用次数: 117
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.