As a doxastic counterpart to epistemic logic based on $\mathbf{S5}$ we study the modal logic $\KS$ that can also be viewed as an approach to modelling a kind of objective and fair belief. We then apply $\KS$ to the problem of minimal beliefs and develop an alternative approach to nonmonotonic modal logic that replaces the usual notion of expansion by a weaker concept, and we show that this corresponds to a certain minimal kind of $\KS$ model. This seems to provide a more intuitive account of nonmonotonic doxastic reasoning. At the same time we can interpret the $\mathbf{S5}$ knowledge operator in $\KS$ in the spirit of {\em justified true belief}.