So, if you look at the “big picture”, the upper bound is exponential. But if you look at it locally, the introduction of new rules and premises makes it combinatorial.

]]>I believe my statement is correct. It grows exponentially w.r.t. the proof length, that is what Marcus Hutter’s famous paper The Fastest and Shortest Algorithm for All Well-Defined Problems says. He means the length of the binary representation of the proof, but I think it applies here too. There is a finite number of rules and axioms, ultimately a inference tree of size S can be turned into a binary string of length O(S).

Maybe you mean w.r.t. to something else. For instance the complexity w.r.t. the length of the theorem is unbounded.

]]>be constructive to present an example of success output and the path

which lead to it? I mean the example of “more interesting things to

emerge” and how we think they could emerge. After having a few such

examples and designing the implementation one could without actual programming

estimate how probably is that the AI would invent such think.

Alternative

approach would be to try to implement it and count on that AI would

surprise us and invent something we didn’t predict. But I’m afraid it is

too optimistic…