 Modal logic can be viewed broadly as the logic of different sorts of modalities, or modes of truth: alethic (“necessarily”), epistemic (“it is known that”), deontic (“it ought to be the case that”), or temporal (“it is always the case that”) among others. Common logical features of these operators justify the common label. In the strict sense however, the term “modal logic” is reserved for the logic of the alethic modalities, as opposed for example to temporal or deontic logic. From a merely technical point of view, any logic with non-truth-functional operators, including first-order logic, can be regarded as a modal logic: in this perspective the quantifiers too can be regarded as modal operators (as in Montague 1960). Nonetheless, we follow the traditional understanding of modal logics as not including full-fledged first-order logic. In this perspective it is the modal operators that can be regarded as restricted quantifiers, ranging over special entities like possible worlds or temporal instants. Arthur Prior was one of the first philosophers/logicians to emphasize that the modal system S5 can be translated into a fragment of first-order logic, which he called “the uniform monadic first-order predicate calculus” (Prior and Fine 1977: 56). Monadic, since no relation between worlds needs to be stated for S5; and uniform as only one variable is needed to quantify over worlds (instants) when bound, and to refer to the privileged state (the actual world or the present time) when free (see Prior and Fine 1977). Concerning the technical question of which model-theoretic features characterize modal logics understood as well-behaved fragments of first-order logic, see Blackburn and van Benthem’s “Modal Logic: A Semantic Perspective” (2007a).