Probability Theory Ensues from Assumptions of Approximate Consistency: A Simple Derivation and its Implications for AGI

By slightly tweaking some recent mathematics by Dupré and Tipler, it is shown that, if an intelligence even approximately obeys certain simple consistency conditions in its reasoning about uncertainty, then its uncertainty judgments must approximately obey the rules of probability theory. It is argued that, while real-world cognitive systems will rarely be fully consistent, they will often possess approximate consistency of the sort required by this mathematics. The conclusion is that, much of the time, cognitive systems’ uncertainty judgments will roughly resemble the conclusions of probability theory – with more deviation from probability theory when fewer resources are devoted to the maintenance of consistency. Implications for AGI architecture are briefly discussed, including the viability of hybrid systems that use (explicit or implicit) probabilistic inference when resources are available for adequate consistency maintenance, and other heuristic methods elsewise.