Basing probabilistic logic on gambles

Peter R. Gillett, Richard B. Scherl, Glenn Shafer

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations


This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson’s probabilistic logic and Frisch and Haddawy’s anytime inference procedure with Wilson and Moral’s logic of gambles. Two distinct semantics can be used for our probabilistic logic: (1) the measure-theoretic semantics used by the prior logics already mentioned and also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a behavioral semantics. Under the measure-theoretic semantics, sentences of our probabilistic logic are interpreted as assertions about a probability distribution over interpretations of the underlying logic. Under the behavioral semantics, these sentences are interpreted only as asserting the acceptability of gambles, and this suggests different directions for generalization.

Original languageEnglish (US)
StatePublished - 2005
Event4th International Symposium on Imprecise Probabilities and Their Applications, ISIPTA 2005 - Pittsburgh, United States
Duration: Jul 20 2005Jul 23 2005


Conference4th International Symposium on Imprecise Probabilities and Their Applications, ISIPTA 2005
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Statistics and Probability


  • Anytime Deduction
  • Behavioral Semantics
  • Gambles
  • Measure-theoretic
  • Probabilistic Logic


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