Theorem: Fuzzy beliefs (as in https://www.alignmentforum.org/posts/Ajcq9xWi2fmgn8RBJ/the-credit-assignment-problem#X6fFvAHkxCPmQYB6v ) form a continuous DCPO. (At least I'm pretty sure this is true. I've only given proof sketches so far)

The relevant definitions:

A fuzzy belief over a set X is a concave function ϕ:ΔX→[0,1] such that sup(ϕ)=1 (where ΔX is the space of probability distributions on X). Fuzzy beliefs are partially ordered by ϕ≤ψ⟺∀μ∈ΔX:ϕ(μ)&... (read more)

Theorem: Fuzzy beliefs (as in https://www.alignmentforum.org/posts/Ajcq9xWi2fmgn8RBJ/the-credit-assignment-problem#X6fFvAHkxCPmQYB6v ) form a continuous DCPO. (At least I'm pretty sure this is true. I've only given proof sketches so far)

The relevant definitions:

A fuzzy belief over a set X is a concave function ϕ:ΔX→[0,1] such that sup(ϕ)=1 (where ΔX is the space of probability distributions on X). Fuzzy beliefs are partially ordered by ϕ≤ψ⟺∀μ∈ΔX:ϕ(μ)&... (read more)