However, the approach is designed so that these “spurious” logical implications are unprovable, so they don’t interfere with decision-making. The proof of that is left as an easy exercise.

I don’t think this is technically true as stated; it seems to be possible that the agent proves some spurious counterfactuals as long as the outcome it does in fact obtain is the best possible one. (This is of course harmless!) Say the agent has two possible actions, ¯a(5) and ¯a(10), leading to outcomes ¯o(5) and ¯o(10), respectively. The latter is preferred, and these are the only two outcomes. Suppose that ¯a(10) happens to be lexicographically lower than ¯a(5) in the agent’s reasoning. Then it seems to be provable that the agent will in fact choose ¯a(10), meaning that it’s provable that it won’t choose ¯a(5), meaning that it finds both (¯a(5),¯o(5)) and the spurious (¯a(5),¯o(10)) in the first step.

So I think the correct statement is a disjunction: The agent obtains the highest possible outcome or it finds no spurious counterfactuals.

I don’t think this is technically true as stated; it seems to be possible that the agent proves some spurious counterfactuals as long as the outcome it does in fact obtain is the best possible one. (This is of course harmless!) Say the agent has two possible actions, ¯a(5) and ¯a(10), leading to outcomes ¯o(5) and ¯o(10), respectively. The latter is preferred, and these are the only two outcomes. Suppose that ¯a(10) happens to be lexicographically lower than ¯a(5) in the agent’s reasoning. Then it seems to be provable that the agent will in fact choose ¯a(10), meaning that it’s provable that it

won’tchoose ¯a(5), meaning that it finds both (¯a(5),¯o(5)) and the spurious (¯a(5),¯o(10)) in the first step.So I think the correct statement is a disjunction: The agent obtains the highest possible outcome

orit finds no spurious counterfactuals.Ooh, nice: we don’t need to eliminate all spurious counterfactuals, only the malignant ones!

Yes, that’s correct. Thanks!