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A model consists in one or more possible worlds. Necessity in a world is determined by its associated set of possible worlds.

I am curious whether there is any work that involves an account of something like "possible models."

So, whereas each possible world in a model makes each statement in the model either true or false, similarly, each possible model in a (supermodel?) varies some property of worlds in the supermodel. For example, each world in a model may have R to each other world in that model. In the supermodel it's part of, perhaps another possible model has some worlds failing to have R to each other.

A gloss on a possible model might be "ways the possibility relation could be."

Is this a concept anyone has written near or about?

  • This sounds like two-dimensional modal semantics, where fixed "model" would correspond to fixing one of the modal parameters and only varying the other, see Chalmers, Two-Dimensional Semantics. One needs that to interpret sentences like "it is possible that X is impossible". – Conifold Jul 27 at 0:30
  • Thank you! That's very helpful. – user3752935 Jul 27 at 0:31

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