 Kripke (1959), Fine (1970), and Kaplan (1970) went on to consider systems of propositional modal logic supplemented with propositional quantifiers governed by appropriate axioms and rules of inference. Moreover, they explained how to generalize the Kripkean model theory for propositional modal logic in order to accommodate the presence of propositional quantification. A Kripke model for the language of propositional modal logic is an ordered triple, \(\langle W, R, \mathcal{I} \rangle\), in which \(W\) is a non-empty set of worlds, \(R\) is a binary relation on \(W\), and \(\mathcal{I}\) is an interpretation function, which can be taken to assign a set of possible worlds to each sentence letter in the language. This suggests we interpret propositional quantification in terms of quantification over sets of worlds in \(W\). An assignment of values to the propositional variables \(s\) will map each propositional variable into a set of worlds, and we define satisfaction at a world by an assignment \(s\) as usual, except for an appropriate clause for the quantifier: \(\forall p A\) is satisfied at a world \(w\) in \(W\) in \(\langle W, R, \mathcal{I} \rangle\) by assignment \(s\) if, and only if, \(A\) is satisfied at \(w\) by every assignment \(s[p/S]\) in which \(S\) is a subset of \(W\). The definitions of truth at a world and truth in a Kripke model then proceed as usual.