Reasoning with time and chance

Daniel Lehmann*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

92 Scopus citations

Abstract

The temporal propositional logic of linear time is generalized to an uncertain world, in which random events may occur. The formulas do not mention probabilities explicitly, i.e., the only probability appearing explicitly in formulas is probability one. This logic is claimed to be useful for stating and proving properties of probabilistic programs. It is convenient for proving those properties that do not depend on the specific distribution of probabilities used in the program's random draws. The formulas describe properties of execution sequences. The models are stochastic systems, with state transition probabilities. Three different axiomatic systems are proposed and shown complete for general models, finite models, and models with bounded transition probabilities, respectively. All three systems are decidable, by the results of Rabin (Trans. Amer. Math. Soc. 141 (1969), 1-35).

Original languageEnglish
Pages (from-to)165-198
Number of pages34
JournalInformation and control
Volume53
Issue number3
DOIs
StatePublished - Jun 1982

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