So, we already have the underlying mathematical structure of the first half of cognition (determining the state of the world). What about the second half- influencing the world in a predictable way to achieve goals? We know that this is solvable, given enough computing power and omniscience- just dump the world data into a quantum simulator, run all possible modifications that the optimization process can make, and see which one has the highest expected utility (this, if I understand correctly, is basically what AIXI does).
So, we already have the underlying mathematical structure of the first half of cognition (determining the state of the world). What about the second half- influencing the world in a predictable way to achieve goals? We know that this is solvable, given enough computing power and omniscience- just dump the world data into a quantum simulator, run all possible modifications that the optimization process can make, and see which one has the highest expected utility (this, if I understand correctly, is basically what AIXI does).