Matt, Yes, that is completely true. I should have worded myself more clearly.
Ben, Matt has sorted out the mistake you are referring to. What I meant was that AIXI is incapable of understanding the proof, not that it is incapable of producing it. Another way of describing it: AIXI could learn to accurately mimic the way humans talk about uncomputable entities, but it would never invent these things on its own. --Abram On Sun, Oct 19, 2008 at 4:32 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote: > --- On Sat, 10/18/08, Abram Demski <[EMAIL PROTECTED]> wrote: > >> No, I do not claim that computer theorem-provers cannot >> prove Goedel's Theorem. It has been done. The objection applies >> specifically to AIXI-- AIXI cannot prove goedel's theorem. > > Yes it can. It just can't understand its own proof in the sense of Tarski's > undefinability theorem. > > Construct a "predictive" AIXI environment as follows: the environment output > symbol does not depend on anything the agent does. However, the agent > receives a reward when its output symbol matches the next symbol input from > the environment. Thus, the environment can be modeled as a string that the > agent has the goal of compressing. > > Now encode in the environment a series of theorems followed by their proofs. > Since proofs can be mechanically checked, and therefore found given enough > time (if the proof exists), then the optimal strategy for the agent, > according to AIXI is to guess that the environment receives as input a series > of theorems and that the environment then proves them and outputs the proof. > AIXI then replicates its guess, thus correctly predicting the proofs and > maximizing its reward. To prove Goedel's theorem, we simply encode it into > the environment after a series of other theorems and their proofs. > > -- Matt Mahoney, [EMAIL PROTECTED] > > > > ------------------------------------------- > agi > Archives: https://www.listbox.com/member/archive/303/=now > RSS Feed: https://www.listbox.com/member/archive/rss/303/ > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
