Now some of the `dpm`s we work with will be `bool dpm`s, which are functions from discourse possibilities to `bool`s (and discourse possibilities). It's tempting to think we might just work with `bool dpm`s instead of sets of possibilities. However, I don't think this can work. The reason why is that at a crucial point in GS&Vs semantics, we have to work with not just a *single* way of mutating or "extending" a discourse possibility, but a *range* of different ways to mutate the live discourse possibilities. So we do need to work with sets, after all.
Now some of the `dpm`s we work with will be `bool dpm`s, which are functions from discourse possibilities to `bool`s (and discourse possibilities). It's tempting to think we might just work with `bool dpm`s instead of sets of possibilities. However, I don't think this can work. The reason why is that at a crucial point in GS&Vs semantics, we have to work with not just a *single* way of mutating or "extending" a discourse possibility, but a *range* of different ways to mutate the live discourse possibilities. So we do need to work with sets, after all.