 Kripke semantics for quantified  modal logics,  tense logics,  deontic logics,  intuitionistic logics,  and so on, are often free. This is because they index truth to certain objects that we shall call “worlds,” and usually some things that we have names for do not exist in some of these worlds. Worlds may be conceived in various ways: they may, for example, be understood as possible universes in alethic modal logic, times or moments in tense logic, permissible conditions in deontic logic, or epistemically possible states of knowledge in intuitionistic logic. Associated with each world \(w\) is a domain \(\bD_w\), of objects (intuitively, the set of objects that exist at \(w)\). An object may exist in (or “at”) more than one world but need not exist in all. Thus, for example, Kripke semantics for tense logic represents the fact that Bertrand Russell existed at one time but exists no longer by Russell’s being a member of the domains of certain “worlds”—that is, times (specifically, portions of the last two centuries)—but not others (the present, for example, or all future times). Two natural assumptions are made here: that the same object may exist in more than one world (this is the assumption of transworld identity), and that some singular terms—proper names, in particular—refer not only to an object at a given world, but to that same object at every world. Such terms are called rigid designators. Any logic that combines rigid designators with quantifiers over the domains of worlds in which their referents do not exist must be free.