FWIW, it’s not really clear to me how to map the IR/higher-language analogy into this situation, but when I try to it feels more like belief functionals are the higher-level language and PDGs are a particular lower-level implementation thereof (and from this perspective it doubly makes sense why the map isn’t injective, since there are a wide variety of ways to compile a given higher-level program into a given lower-level representation); I don’t really see how it could be the case that PDGs are less burdensome than belief functionals given that if you want to specify your belief functional with a PDG, you’re always free to do so, and given that you’re also free to do so with simpler techniques (e.g. all of the items under ”...to express beliefs” in the original post, which are IMO much simpler to express with belief functionals that aren’t PDGs).
Regardless, I do find your argument at the end (“in my view [...] had a flaw)”) quite compelling; I think we’re on the same page about belief-revision being an extremely important aspect of belief-modeling, and if there’s in fact not a clear way to do this sort of credit assignment for belief functionals then it does make them significantly less attractive than PDGs for understanding belief dynamics.
FWIW, it’s not really clear to me how to map the IR/higher-language analogy into this situation, but when I try to it feels more like belief functionals are the higher-level language and PDGs are a particular lower-level implementation thereof (and from this perspective it doubly makes sense why the map isn’t injective, since there are a wide variety of ways to compile a given higher-level program into a given lower-level representation); I don’t really see how it could be the case that PDGs are less burdensome than belief functionals given that if you want to specify your belief functional with a PDG, you’re always free to do so, and given that you’re also free to do so with simpler techniques (e.g. all of the items under ”...to express beliefs” in the original post, which are IMO much simpler to express with belief functionals that aren’t PDGs).
Regardless, I do find your argument at the end (“in my view [...] had a flaw)”) quite compelling; I think we’re on the same page about belief-revision being an extremely important aspect of belief-modeling, and if there’s in fact not a clear way to do this sort of credit assignment for belief functionals then it does make them significantly less attractive than PDGs for understanding belief dynamics.