A logical view of probability
Nic Wilson, Serafı́n Moral · 1994
Imprecise Probability (or Upper and Lower Probability) is represented as a very simple but powerful logic. Despite having a very different language from classical logics, it enjoys many of the most important properties, which means that some extensions to classical logic can be applied in a fairly straightforward way. The logic is extended to allow qualitative grades of belief, which can be used to represent degrees of caution, and this is applied to create theories of belief revision and non-monotonic inference for probability statements. We also construct a theory of default probability which is based on a variant of Reiter's default logic; this can be used to express and reason with default probability statements.