These general "multicomputational processes" are well known in computer science as nondeterministic transition systems, or coalgebras for the powerset functor. And in that setting there is a lot of work that has been done about the kinds of logical statement that can be said about their evolution -- such as whether a given proposition about the states may always or eventually hold; this is coalgebraic modal logic. As usual, Wolfram does not mention this prior work.

One thing that I have often thought though is that the mathematical sciences could do with more cross-pollination with coalgebra.