The notion of global supervenience captures the idea that the overall distribution of certain properties in the world is fixed by the overall distribution of certain other properties. A formal implementation of this idea in constant-domain Kripke models is as follows: predicates $Q_1,\dots ,Q_m$ globally supervene on predicates $P_1,\dots ,P_n$ in world w if two successors of w cannot differ with respect to the extensions of the $Q_i$ without also differing with respect to the extensions of the $P_i$. Equivalently: relative to the successors of w, the extensions of the $Q_i$ are functionally determined by the extensions of the $P_i$. In this paper, we study this notion of global supervenience, achieving three things. First, we prove that claims of global supervenience cannot be expressed in standard modal predicate logic. Second, we prove that they can be expressed naturally in an inquisitive extension of modal predicate logic, where they are captured as strict conditionals involving questions; as we show, this also sheds light on the logical features of global supervenience, which are tightly related to the logical properties of strict conditionals and questions. Third, by making crucial use of the notion of coherence, we prove that the relevant system of inquisitive modal logic is compact and has a recursively enumerable set of validities; these properties are non-trivial, since in this logic a strict conditional expresses a second-order quantification over sets of successors.