概率命题时间逻辑

Q4 Mathematics
Sergiu Hart, Micha Sharir
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引用次数: 49

摘要

我们提出了两个(密切相关的)基于分支时间时间逻辑的命题概率时间逻辑,这是由Ben-Ari, Pnueli和Manna (Acta Inform. 20 (1983), 207-226), Emerson和Halpern(“Proceedings,第14届ACM研讨会”)介绍的。《计算机理论》, 1982年,第169-179页,爱默生和克拉克(Sci。第一版。程序2(1982),241-266)。第一个逻辑,PTLf,是在有限模型上解释的,而第二个逻辑,PTLb,是第一个逻辑的扩展,是在无限模型上解释的,转移概率有界远离0。逻辑PTLf允许我们对有限状态顺序概率程序进行推理,逻辑PTLb允许我们对(有限状态)并发概率程序进行推理,而无需显式引用其状态转移概率的实际值。对表法的推广,给出了确定的单指数时间决策过程,并给出了它们的完全公理化。讨论了PTLb的有限模型性质的不存在性,以及PTLb的可满足公式与有限状态并发概率规划之间的联系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Probabilistic propositional temporal logics

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.

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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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