{"title":"概率命题时间逻辑","authors":"Sergiu Hart, Micha Sharir","doi":"10.1016/S0019-9958(86)80001-8","DOIUrl":null,"url":null,"abstract":"<div><p>We present two (closely-related) propositional probabilistic temporal logics based on temporal logics of branching time as introduced by Ben-Ari, Pnueli, and Manna (<em>Acta Inform.</em> <strong>20</strong> (1983), 207–226), Emerson and Halpern (“Proceedings, 14th ACM Sympos. Theory of Comput.,” 1982, pp. 169–179, and Emerson and Clarke (<em>Sci. Comput. Program.</em> <strong>2</strong> (1982), 241–266). The first logic, <em>PTL<sub>f</sub></em>, is interpreted over finite models, while the second logic, <em>PTL<sub>b</sub></em>, which is an extension of the first one, is interpreted over infinite models with transition probabilities bounded away from 0. The logic <em>PTL<sub>f</sub></em> allows us to reason about finite-state sequential probabilistic programs, and the logic <em>PTL<sub>b</sub></em> allows us to reason about (finite-state) concurrent probabilistic programs, without any explicit reference to the actual values of their state-transition probabilities. A generalization of the tableau method yields deterministic single-exponential time decision procedures for our logics, and complete axiomatizations of them are given. Several meta-results, including the absence of a finite-model property for <em>PTL<sub>b</sub></em>, and the connection between satisfiable formulae of <em>PTL<sub>b</sub></em> and finite state concurrent probabilistic programs, are also discussed.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80001-8","citationCount":"49","resultStr":"{\"title\":\"Probabilistic propositional temporal logics\",\"authors\":\"Sergiu Hart, Micha Sharir\",\"doi\":\"10.1016/S0019-9958(86)80001-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present two (closely-related) propositional probabilistic temporal logics based on temporal logics of branching time as introduced by Ben-Ari, Pnueli, and Manna (<em>Acta Inform.</em> <strong>20</strong> (1983), 207–226), Emerson and Halpern (“Proceedings, 14th ACM Sympos. Theory of Comput.,” 1982, pp. 169–179, and Emerson and Clarke (<em>Sci. Comput. Program.</em> <strong>2</strong> (1982), 241–266). The first logic, <em>PTL<sub>f</sub></em>, is interpreted over finite models, while the second logic, <em>PTL<sub>b</sub></em>, which is an extension of the first one, is interpreted over infinite models with transition probabilities bounded away from 0. The logic <em>PTL<sub>f</sub></em> allows us to reason about finite-state sequential probabilistic programs, and the logic <em>PTL<sub>b</sub></em> allows us to reason about (finite-state) concurrent probabilistic programs, without any explicit reference to the actual values of their state-transition probabilities. A generalization of the tableau method yields deterministic single-exponential time decision procedures for our logics, and complete axiomatizations of them are given. Several meta-results, including the absence of a finite-model property for <em>PTL<sub>b</sub></em>, and the connection between satisfiable formulae of <em>PTL<sub>b</sub></em> and finite state concurrent probabilistic programs, are also discussed.</p></div>\",\"PeriodicalId\":38164,\"journal\":{\"name\":\"信息与控制\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1986-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80001-8\",\"citationCount\":\"49\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"信息与控制\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019995886800018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
We present two (closely-related) propositional probabilistic temporal logics based on temporal logics of branching time as introduced by Ben-Ari, Pnueli, and Manna (Acta Inform.20 (1983), 207–226), Emerson and Halpern (“Proceedings, 14th ACM Sympos. Theory of Comput.,” 1982, pp. 169–179, and Emerson and Clarke (Sci. Comput. Program.2 (1982), 241–266). The first logic, PTLf, is interpreted over finite models, while the second logic, PTLb, which is an extension of the first one, is interpreted over infinite models with transition probabilities bounded away from 0. The logic PTLf allows us to reason about finite-state sequential probabilistic programs, and the logic PTLb allows us to reason about (finite-state) concurrent probabilistic programs, without any explicit reference to the actual values of their state-transition probabilities. A generalization of the tableau method yields deterministic single-exponential time decision procedures for our logics, and complete axiomatizations of them are given. Several meta-results, including the absence of a finite-model property for PTLb, and the connection between satisfiable formulae of PTLb and finite state concurrent probabilistic programs, are also discussed.