Logics with lower and upper probability operators

摘要

We present a first-order and a propositional logic with unary operators that speak about upper and lower probabilities. We describe the corresponding class of models, and we discuss decidability issues for the propositional logic. We provide infinitary axiomatizations for both logics and we prove that the axiomatizations are sound and strongly complete. For some restrictions of the logics we provide finitary axiomatic systems.(1) (C) 2017 Published by Elsevier Inc.