I’ll just note that in a modal logic or halting oracle setting you don’t need the chicken rule, as we found in this old post: https://agentfoundations.org/item?id=4 So it seems like at least the first problem is about the approximation, not the thing being approximated.
Yeah, the 5 and 10 problem in the post actually can be addressed using provability ideas, in a way that fits in pretty natually with logical induction. The motivation here is to work with decision problems where you can’t prove statements A=a→U=u for agent A, utility function U, action a, and utility value u, at least not with the amount of computing power provided, but you want to use inductive generalizations instead. That isn’t necessary in this example, so it’s more of an illustration.
To say a bit more, if you make logical inductors propositionally consistent, similarly to what is done in this post, and make them assign things that have been proven already probability 1, then they will work on the 5 and 10 problem in the post.
It would be interesting if there was more of an analogy to explore between the provability oracle setting and the inductive setting, and more ideas could be carried over from modal UDT, but it seems to me that this is a different kind of problem that will require new ideas.
I’ll just note that in a modal logic or halting oracle setting you don’t need the chicken rule, as we found in this old post: https://agentfoundations.org/item?id=4 So it seems like at least the first problem is about the approximation, not the thing being approximated.
Yeah, the 5 and 10 problem in the post actually can be addressed using provability ideas, in a way that fits in pretty natually with logical induction. The motivation here is to work with decision problems where you can’t prove statements A=a→U=u for agent A, utility function U, action a, and utility value u, at least not with the amount of computing power provided, but you want to use inductive generalizations instead. That isn’t necessary in this example, so it’s more of an illustration.
To say a bit more, if you make logical inductors propositionally consistent, similarly to what is done in this post, and make them assign things that have been proven already probability 1, then they will work on the 5 and 10 problem in the post.
It would be interesting if there was more of an analogy to explore between the provability oracle setting and the inductive setting, and more ideas could be carried over from modal UDT, but it seems to me that this is a different kind of problem that will require new ideas.