Action and observation are not "intuitively" dual, to my first thought they are invariant on time reversal. Action is a state-transition of the environment, and observation is a state-transition of the agent. I can see how the duality can be suggested by viewing action as a move of the agent-player and observation as a move of the environment-player. But here duality is in that a node which in one direction was a move by A (associated with arrows to the right), in the other direction is a move by E (associated with arrows to the left).