Game semantics etc. were part of a search that was answered by ADT (alternatively, finally understanding UDT); they are failing to answer this question in the sense of exploring explicit counterfactuals, rather than explaining where counterfactuals come from.

After that, I tried building on ADT, didn't get very far, then tried figuring out epistemic role of observations (which UDT/ADT deny), and I think was successful (the answer being a kind of "universal" platonism where physical facts are seen as non-special, logical theories as machines for perceiving abstract facts normally external to themselves, and processes as relating facts along their way, which generalize to ways of knowing physical facts, as in causality; this ontological stance seems very robust and describes all sorts of situations satisfactorily). This as yet needs better toy models as examples, or better-defined connection to standard math, which I'm currently trying to find.