  We determine the modal logic of fixed-point models of truth and their
axiomatizations by Solomon Feferman via Solovay-style completeness results.
Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we
find a modal logic $M$ such that a modal sentence $\varphi$ is a theorem of $M$
if and only if the sentence $\varphi^*$ obtained by translating the modal
operator with the truth predicate is true in $\mathcal{M}$ or a theorem of $S$
under all such translations. To this end, we introduce a novel version of
possible worlds semantics featuring both classical and nonclassical worlds and
establish the completeness of a family of non-congruent modal logics whose
internal logic is subclassical with respect to this semantics.
