I think things will come together more if you switch from treating facts as partitions of real external parallel worlds, to partitions of models of the world inside your head. Worlds aren’t probabilistic (more or less), but models can be. Proofs don’t change what math is true, but they can change what math you need to model as true. Etc.
I agree that the “environment” here should be thought of as the agent’s subjective beliefs about the environment. The “coulds” have to be a sort of subjective possibility. I suspect “coulds” are just what cannot be ruled out by an underlying proof process, and probabilities are the “caring function” over the remaining possibilities which allows choice.
I think things will come together more if you switch from treating facts as partitions of real external parallel worlds, to partitions of models of the world inside your head. Worlds aren’t probabilistic (more or less), but models can be. Proofs don’t change what math is true, but they can change what math you need to model as true. Etc.
I agree that the “environment” here should be thought of as the agent’s subjective beliefs about the environment. The “coulds” have to be a sort of subjective possibility. I suspect “coulds” are just what cannot be ruled out by an underlying proof process, and probabilities are the “caring function” over the remaining possibilities which allows choice.