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Probabilistic Gödel Machine Hardware

Above we have focused on an example deterministic machine. It is straight-forward to extend this to computers whose actions are computed in probabilistic fashion, given the current state. Then the expectation calculus used for probabilistic aspects of the environment simply has to be extended to the hardware itself, and the mechanism for verifying proofs has to take into account that there is no such thing as a certain theorem--at best there are formal statements which are true with such and such probability. In fact, this may be the most realistic approach as any physical hardware is error-prone, which should be taken into account by realistic probabilistic Gödel machines.

Probabilistic settings also automatically avoid certain issues of axiomatic consistency. For example, predictions proven to come true with probability less than 1.0 do not necessarily cause contradictions even when they do not match the observations.

Juergen Schmidhuber 2005-01-03