Reasoning about knowledge and probability
Ronald Fagin, Joseph Yehuda Halpern · Journal of the ACM · 1994
IBM AInuzdetz Resecrrcb Center, SCZnJo.w,Cul[fomia Abstroct.We provide a model for rcusonmg about knowledge and prob~bility together, We allow explicit mention of probabilities in formulas, so that our kmguagc has formu]as that essentially say "according to agent ~, formula p holds with probabi]lty at least b " The langutigc IS powerful enough to allow rewoning about higher-order proixibdities, as well w ti]lowing e~pliclt comparisons of the probabilities an agent places on distinct events.We present a general framcw(>rk for interpreting such formulas, and consider wmous properties that might hold of the interrclatmnship between agents' probability assignments at different states.We pro~,icte a complete axlomatization for reasoning about knowledge and probabihty, prove a small model property, and obtain decision procedures, We then consider the effects of adding common knowledge and a probabilistic variant of common knowledge to the language.