The Modal Logic of the Calculus of Probability

Abstract

A new class of models which does not require an additional operator on the Boolean algebra of formulas to capture some notion of necessity, possibility, and impossibility is introduced and investigated. These models permit to combine efficiently logic and probability via a bridge principle. In particular, a second intension to the mode of impossibility resolves, canonically, the problem of the existence of almost identical events, which are usually considered equivalent. In fact, these events reveal a critical aspect of uncertainty; their systematic study in relation to uncertainty modelling is the domain of formal agnoiology.