I think the sense in which logical inductors are a robustness result is much stronger than the connection between Bayes and robustness. The dutch books are just an argument that if you are not coherent, you could be money pumped. They are not even the most convincing argument for coherence in my opinion. Logical inductors on the other hand are directly getting good behavior in reasoning about logic by explicitly stopping adversaries in my reasoning process from making a specific kind of treacherous turn.
In my view logical inductors are an application of a general purpose robust learning framework to logic. Most of the stuff in the logical induction paper could have been done in a domain other than logic, and most of the insights are not about logic. Instead, the insights are about a way of aggregating a bunch of experts that allow them to watch over each other and bet against the adversarial experts when they try to make a treacherous turn.
Logic is a very rich domain that we needed to understand in order to think about naturalized agency. However, since it is so large and rich, it contains adversaries, and normal ways of doing induction were not robust to these adversaries pushing you around (like in the all mathematicians are rollable thing). Logical inductions stepped in as a way to get good local results in logic without letting the adversaries take over. (Or at least it was slightly more robust than other approaches. It still does not solve benign induction.) Then, we used logical induction for reasoning about naturalized agency and a bunch of fruit came out, but those are just the applications. At the heart, logical inductors are a robustness result that is not about logic. (Although our methods for solving the robustness problem were very naturalized in flavor.)
I think the sense in which logical inductors are a robustness result is much stronger than the connection between Bayes and robustness. The dutch books are just an argument that if you are not coherent, you could be money pumped. They are not even the most convincing argument for coherence in my opinion. Logical inductors on the other hand are directly getting good behavior in reasoning about logic by explicitly stopping adversaries in my reasoning process from making a specific kind of treacherous turn.
In my view logical inductors are an application of a general purpose robust learning framework to logic. Most of the stuff in the logical induction paper could have been done in a domain other than logic, and most of the insights are not about logic. Instead, the insights are about a way of aggregating a bunch of experts that allow them to watch over each other and bet against the adversarial experts when they try to make a treacherous turn.
Logic is a very rich domain that we needed to understand in order to think about naturalized agency. However, since it is so large and rich, it contains adversaries, and normal ways of doing induction were not robust to these adversaries pushing you around (like in the all mathematicians are rollable thing). Logical inductions stepped in as a way to get good local results in logic without letting the adversaries take over. (Or at least it was slightly more robust than other approaches. It still does not solve benign induction.) Then, we used logical induction for reasoning about naturalized agency and a bunch of fruit came out, but those are just the applications. At the heart, logical inductors are a robustness result that is not about logic. (Although our methods for solving the robustness problem were very naturalized in flavor.)