Logics of Imprecise Comparative Probability

In this talk, based on joint work with Yifeng Ding and Thomas Icard (at https://escholarship.org/uc/item/1m3156ps), I will discuss a logical perspective on connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability and comparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures.