 One possible response is to reject (2). Leeb (2006) develops for a version of PFL a dual-domain semantics in which the extensions of formulas are abstract states of affairs. In this semantics, co-referential open sentences are exchangeable not salve veritate, but (as he puts it) salve extensione; that is, the exchange does not alter the state of affairs designated by the statement in which it occurs. But Leeb’s state-of-affairs semantics is so complex that it may discourage application.