Representing upper probability Measures over rational Lukasiewicz logic

Abstract

Upper probability measures are measures of uncertainty that generalize probability measures in order to deal with non-measurable events. Following an approach that goes back to previous works by H ajek, Esteva, and Godo, we show how to expand Rational Lukasiewicz Logic by modal operators in order to reason about upper probabilities of classical Boolean events ' so that ( ' ) can be read as \the upper probability of ' ". We build the logic U (R L) for representing upper probabilities and show it to be complete w.r.t. a class of Kripke structures equipped with an upper probability measure. Finally, we prove that the set of U (R L)-satis able formulas is NP-complete.