  A limitation of the permutation invariance criterion (as it has been stated so far) is that it applies only to extensional operators and connectives. It is therefore of no help in deciding, for instance, whether the necessity operator in S4 modal logic or the H operator (“it has always been the case that”) in temporal logic are bona fide logical constants, and these are among the questions that we wanted a criterion to resolve. However, the invariance criterion can be extended in a natural way to intensional operators. The usual strategy for handling such operators semantically is to relativize truth not just to an assignment of values to variables, but also to a possible world and a time. In such a framework, one might demand that logical constants be insensitive not just to permutations of the domain of objects, but to permutations of the domain of possible worlds and the domain of times (see Scott 1970, 161, McCarthy 1981, 511–13, van Benthem 1989, 334). The resulting criterion is fairly stringent: it counts the S5 necessity operator as a logical constant, but not the S4 necessity operator or the H operator in temporal logic. The reason is that the latter two operators are sensitive to structure on the domains of worlds and times—the “accessibility relation” in the former case, the relation of temporal ordering in the latter—and this structure is not preserved by all permutations of these  domains.[15]  (See the entries on   modal logic  and  temporal logic.)