Have any philosophers come up with a workable formal, mathematical definition for what the laws of an arbitrary physical universe might be? Such a definition would need to allow specification of different possible laws of physics, as well as the actual current universe state or history. It would need to be as general as possible, not tied down to any particular theory of physics. And it would need to allow us to reason about it mathematically, e.g. defining morphisms between different possible laws.
As an example of the kind of thing I'm looking for, consider this definition:
The laws of a physical universe are a set of propositions P that may hold within possible universes that obey the laws, and a set of subsets of P, interpreted as saying that for each subset, there is a universe obeying the laws in which all elements of that subset hold.
Or this one:
The laws of a physical universe are given by a set X of instantaneous states, and a function δ: X, R -> X where δ(x, t) gives the new state of the universe from initial state x after time t has passed, subject to the constraint δ(δ(x, t1), t2) = δ(x, t1+t2).
Or this one:
The laws of a physical universe are a set of propositions P, and a set of directed acyclic graphs with nodes labeled in P, with the edges indicating causation relationships.