  Consider a version of Kripke models in which a separate domain is associated with each state of the model. At each state, quantifiers are thought of as ranging over the domain associated with that state. This has come to be known as an actualist semantics. Think of the domain associated with a state as the things that actually exist at that state. Thus, for example, in the so-called real world the Great Pyramid of Khufu is in the domain, but the Lighthouse of Alexandria is not. If we were considering the world of, say, 1300, both would be in the domain. In an actualist approach, we need to come to some decision on what to do with formulas containing references to things that exist in other states but not in the state we are considering. Several approaches are plausible; we could take such formulas to be false, or we could take them to be meaningless, for instance, but this seems to be unnecessarily restrictive. After all, we do say things like “the Lighthouse of Alexandria no longer exists,” and we think of it as true. So, the formal version that seems most useful takes quantifiers as ranging over domains state by state, but otherwise allows terms to reference members of any domain. The resulting semantics is often called varying domain as well as actualist.