{"title":"线性时态逻辑满足性的 SAT Meets Tableaux","authors":"Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato","doi":"10.1007/s10817-023-09691-1","DOIUrl":null,"url":null,"abstract":"<p><i>Linear temporal logic</i> (<span>\\(\\textsf{LTL}\\,\\)</span>) and its variant interpreted on <i>finite traces</i> (<span>\\(\\textsf{LTL}_{\\textsf{f}\\,}\\)</span>) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for <span>\\(\\textsf{LTL}\\,\\)</span>and <span>\\(\\textsf{LTL}_{\\textsf{f}\\,}\\)</span>formulas, for which many techniques have been devised during the last decades. Among these are <i>tableau systems</i>, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for <span>\\(\\textsf{LTL}\\,\\)</span>and <span>\\(\\textsf{LTL}_{\\textsf{f}\\,}\\)</span>satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"24 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SAT Meets Tableaux for Linear Temporal Logic Satisfiability\",\"authors\":\"Luca Geatti, Nicola Gigante, Angelo Montanari, Gabriele Venturato\",\"doi\":\"10.1007/s10817-023-09691-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><i>Linear temporal logic</i> (<span>\\\\(\\\\textsf{LTL}\\\\,\\\\)</span>) and its variant interpreted on <i>finite traces</i> (<span>\\\\(\\\\textsf{LTL}_{\\\\textsf{f}\\\\,}\\\\)</span>) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for <span>\\\\(\\\\textsf{LTL}\\\\,\\\\)</span>and <span>\\\\(\\\\textsf{LTL}_{\\\\textsf{f}\\\\,}\\\\)</span>formulas, for which many techniques have been devised during the last decades. Among these are <i>tableau systems</i>, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for <span>\\\\(\\\\textsf{LTL}\\\\,\\\\)</span>and <span>\\\\(\\\\textsf{LTL}_{\\\\textsf{f}\\\\,}\\\\)</span>satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.</p>\",\"PeriodicalId\":15082,\"journal\":{\"name\":\"Journal of Automated Reasoning\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Automated Reasoning\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s10817-023-09691-1\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Automated Reasoning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10817-023-09691-1","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
SAT Meets Tableaux for Linear Temporal Logic Satisfiability
Linear temporal logic (\(\textsf{LTL}\,\)) and its variant interpreted on finite traces (\(\textsf{LTL}_{\textsf{f}\,}\)) are among the most popular specification languages in the fields of formal verification, artificial intelligence, and others. In this paper, we focus on the satisfiability problem for \(\textsf{LTL}\,\)and \(\textsf{LTL}_{\textsf{f}\,}\)formulas, for which many techniques have been devised during the last decades. Among these are tableau systems, of which the most recent is Reynolds’ tree-shaped tableau. We provide a SAT-based algorithm for \(\textsf{LTL}\,\)and \(\textsf{LTL}_{\textsf{f}\,}\)satisfiability checking based on Reynolds’ tableau, proving its correctness and discussing experimental results obtained through its implementation in the BLACK satisfiability checker.
期刊介绍：
The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning.
The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.
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