A first-order logic for reasoning about higher-order upper and lower probabilities

Abstract

We present a first-order probabilistic logic for reasoning about the uncertainty of events modeled by sets of probability measures. In our language, we have formulas that essentially say that “according to agent Ag, for all x, formula α(x) holds with the lower probability at least 1/3 ”. Also, the language is powerful enough to allow reasoning about higher order upper and lower probabilities. We provide corresponding Kripke-style semantics, axiomatize the logic and prove that the axiomatization is sound and strongly complete (every satisfiable set of formulas is consistent).