I propose that we can use a single operator to replace both the □ and ◇ operators used in traditional modal logics (both alethic and deontic), and furthermore that that single operator can also serve a much broader logical function, and also yield a temporal modal logic, dealing with things being or not being the case differently at different times, as well as a spatial modal logic, dealing with things being or not being the case differently at different places.

This single operator I propose establishes the scope of contexts wherein a state of affairs is considered to be, and so might be written as something like at().

This function takes two arguments: the first is a set of contexts, such as places, times, or possible worlds, where some state of affairs is considered to be; and the second is the state of affairs itself, e.g. the state of affairs of "all men being mortal". So we might want to talk about, for instance, the idea of all men in Greece specifically being mortal, and so write to encode that idea. Or if we want to talk about the idea of all men in the past having been mortal, we might write to encode that idea. But most usefully, if that first argument is just the empty set, what you end up encoding is the idea of that state of affairs never, anywhere, at any time, in any possible world, being the case, which is to say, the idea of it being impossible.

With that way of talking about something being impossible, we automatically have a way of talking about it being possible, by negating that formula; and of talking about it being necessary, by applying that impossibility function to the negation of the original state of affairs; and of talking about it being contingent, if we negate that formula in turn.

(Which then yields also functions for impermissibility, permissibility, obligatoriety, and omissibility, if we wrap that idea in a prescriptive mood function rather than a descriptive one.)

By being more specific about the contexts specified, limiting ourselves to specifying sets of times, we can also say things about some state of affairs being the case at all times or some times or no times, without saying anything about all possible worlds, yielding a temporal modal logic (either an alethic temporal logic or a deontic one depending on what mood function we wrap the idea in); and if we instead limit ourselves to specifying sets of places, we can say things about some state of affairs being the case everywhere or somewhere or nowhere, likewise yielding a spatial modal logic (and again, either an alethic or deontic one, as we like).

With our mood functions allowing us to instead express rather than impress these ideas, we can also easily create things like a doxastic or epistemic modal logic, having to do with things like belief and certainty rather than truth and necessity. And lastly, by specifying some fraction of possible worlds, or times, or places, this function can also serve to encode statements about probability, to say talk about things being likely or unlikely (which is to say, them being the case in many or few possible worlds) rather than strictly necessary or impossible (the case in all or no possible worlds); or, combined with the temporal or spatial possibilities, to talk about things being the case most of the time, most places, etc.

The possible modal ideas expressible with this one at() function (plus the mood functions) vastly outnumber those expressible with the traditional □ and ◇ functions.