I think it’s worth mentioning that part of the original appeal of the term (which made us initially wary) was the way it matches intuitively with the experience of signaling behavior. Here’s the original motivating example. Imagine that you are in the Parfit’s Hitchhiker scenario and Paul Ekman has already noticed that you’re lying. What do you do? You try to get a second chance. But it won’t be enough to simply re-state that you’ll pay him. Even if he doesn’t detect the lie this time around, you’re the same person who had to lie only a moment ago. What changed? Well, you want to signal that what’s changed is that some logical time has passed. A logically earlier version of you got a ride from a logically earlier Ekman but didn’t pay. But then Ekman put effort into remembering the logical past and learning from it. A logically more recent version of you wasn’t expecting this, and perished in the desert. Given that both you and Ekman know these things, what you need to do in order to survive is to show that you are in the logical future of those events, and learned from them. Not only that, but you also want to show that you won’t change your mind during the ride back to civilization. There will be time to think during the car ride, and thinking can be a way of getting into the logical future. You want to demonstrate that you’re fully in the logical future of the (chronologically yet-to-be-made) decision to pay.
This might be an easy problem if the hitchhiker and Ekman shared the same concept of logical time (and knew it). Then it would be similar to proving you remembered the literal past; you could describe a trivial detail or an agreed-upon signal. However, agents are not necessarily incentivized (or able) to use a shared imaginary iterated version of whatever game they’re playing. To me it seems like one of the real questions the logical time terminology brings up is, when, and to what extent, will agents be incentivized to use compatible notions of logical time?
I think it’s worth mentioning that part of the original appeal of the term (which made us initially wary) was the way it matches intuitively with the experience of signaling behavior. Here’s the original motivating example. Imagine that you are in the Parfit’s Hitchhiker scenario and Paul Ekman has already noticed that you’re lying. What do you do? You try to get a second chance. But it won’t be enough to simply re-state that you’ll pay him. Even if he doesn’t detect the lie this time around, you’re the same person who had to lie only a moment ago. What changed? Well, you want to signal that what’s changed is that some logical time has passed. A logically earlier version of you got a ride from a logically earlier Ekman but didn’t pay. But then Ekman put effort into remembering the logical past and learning from it. A logically more recent version of you wasn’t expecting this, and perished in the desert. Given that both you and Ekman know these things, what you need to do in order to survive is to show that you are in the logical future of those events, and learned from them. Not only that, but you also want to show that you won’t change your mind during the ride back to civilization. There will be time to think during the car ride, and thinking can be a way of getting into the logical future. You want to demonstrate that you’re fully in the logical future of the (chronologically yet-to-be-made) decision to pay.
This might be an easy problem if the hitchhiker and Ekman shared the same concept of logical time (and knew it). Then it would be similar to proving you remembered the literal past; you could describe a trivial detail or an agreed-upon signal. However, agents are not necessarily incentivized (or able) to use a shared imaginary iterated version of whatever game they’re playing. To me it seems like one of the real questions the logical time terminology brings up is, when, and to what extent, will agents be incentivized to use compatible notions of logical time?