Yes, modal logic seems to be the most natural setting for these kinds of ideas. Also the “chicken rule” from the usual oracle formulations is gone now, I can’t remember why we needed it anymore.
In a probabilistic setting (with a prior over logical theories), EDT wants to condition on the possible actions with a Bayesian conditional, in order to then find the expected utility of each action.
If the agent can prove that it will take a particular action, then conditioning on this action may yield inconsistent stuff (divide-by-zero error for Bayesian conditional). This makes the result ill-defined.
The chicken rule makes this impossible, ensuring that the conditional probabilities are well defined.
So, the chicken rule at least seems useful for EDT.
A model of UDT with a halting oracle searches only for one utility value for each action. I’m guessing the other formulation just wasn’t obvious at the time? (I don’t remember realizing the possibility of playing chicken implicitly before Will Sawin advertised it to me, though I think he attributed it to you.)
Yes, modal logic seems to be the most natural setting for these kinds of ideas. Also the “chicken rule” from the usual oracle formulations is gone now, I can’t remember why we needed it anymore.
In a probabilistic setting (with a prior over logical theories), EDT wants to condition on the possible actions with a Bayesian conditional, in order to then find the expected utility of each action.
If the agent can prove that it will take a particular action, then conditioning on this action may yield inconsistent stuff (divide-by-zero error for Bayesian conditional). This makes the result ill-defined.
The chicken rule makes this impossible, ensuring that the conditional probabilities are well defined.
So, the chicken rule at least seems useful for EDT.
A model of UDT with a halting oracle searches only for one utility value for each action. I’m guessing the other formulation just wasn’t obvious at the time? (I don’t remember realizing the possibility of playing chicken implicitly before Will Sawin advertised it to me, though I think he attributed it to you.)