A logic with upper and lower probability operators

Abstract

© 2015 Proceedings of the 9th International Symposium on Imprecise Probability. We present a propositional logic with unary operators that speak about upper and lower probabilities. We describe the corresponding class of models and discuss decidability issues. We provide an infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete. For some restrictions of the logic we provide finitary axiomatic systems.