  A probabilistic propositional logic, endowed with an epistemic component for
asserting (non-)compatibility of diagonizable and bounded observables, is
presented and illustrated for reasoning about the random results of projective
measurements made on a given quantum state. Simultaneous measurements are
assumed to imply that the underlying observables are compatible. A sound and
weakly complete axiomatization is provided relying on the decidable first-order
theory of real closed ordered fields. The proposed logic is proved to be a
conservative extension of classical propositional logic.
