  Possibilist semantics is simpler to deal with than the actualist version—we have one domain instead of many for quantifiers to range over. And it turns out that if we adopt a possibilist approach, the actualist semantics can be simulated. Suppose we have a single domain of quantification, possibilia, and a special predicate, \(E\), which we think of as true, at each state, of the things that actually exist at that state. If \(\forall\) is a quantifier over the domain of possibilia, we can think of the relativized quantifier, \(\forall\)x\((E(x) \supset \ldots )\) as corresponding to actualist quantification. (We need to assume that, at each state, \(E\) is true of something—this corresponds to assuming domains are non-empty.) This gives an embedding of the actualist semantics into the possibilist one, a result that can be formally stated and proved. Here possibilist semantics will be used, and we assume we have an existence predicate \(E\) available.