If I try to use this framework to express two agents communicating, I get an image with a V1, A1, P1, V2, A2, and P2, with cross arrows from A1 to P2 and A2 to P1. This admits many ways to get a roundtrip message. We could have A1 → P2 → A2 → P2 directly, or A1 → P2 → V2 → A2 → P1, or many cycles among P2, V2, and A2 before P1 receives a message. But in none of these could I hope to get a response in one time step the way I would if both agents simultaneously took an action, and then simultaneously read from their inputs and their current state to get their next state. So I have this feeling that pi : S → Action and update : Observation x S → S already bake in this active/passive distinction by virtue of the type signature, and this framing is maybe just taking away the computational teeth/specificity. And I can write the same infiltration and exfiltration formulas by substituting S_t for V_t, Obs_t for P_t, Action_t for A_t, and S_env_t for E_t.
If I try to use this framework to express two agents communicating, I get an image with a V1, A1, P1, V2, A2, and P2, with cross arrows from A1 to P2 and A2 to P1. This admits many ways to get a roundtrip message. We could have A1 → P2 → A2 → P2 directly, or A1 → P2 → V2 → A2 → P1, or many cycles among P2, V2, and A2 before P1 receives a message. But in none of these could I hope to get a response in one time step the way I would if both agents simultaneously took an action, and then simultaneously read from their inputs and their current state to get their next state. So I have this feeling that pi : S → Action and update : Observation x S → S already bake in this active/passive distinction by virtue of the type signature, and this framing is maybe just taking away the computational teeth/specificity. And I can write the same infiltration and exfiltration formulas by substituting S_t for V_t, Obs_t for P_t, Action_t for A_t, and S_env_t for E_t.
I take back the part about pi and update determining the causal structure, because many causal diagrams are constant with the same poly diagram