On Sat, Mar 1, 2008 at 5:23 PM, daniel radetsky <[EMAIL PROTECTED]> wrote:
> [...] > > > My thinking is that a more-universal theoretical prior would be a prior > > over logically definable models, some of which will be incomputable. > > > I'm not exactly sure what you're talking about, but I assume that these > logically definable models would be defined in some formal language, which > means that they would be caught by Solomnoff. > > Daniel > Not so! The incomputable models I'm referring to would be defined in some formal language, yes. But this does NOT imply that they will be captured by Solomonoff induction! To give a silly example: The busy beaver function is defined for each x as: BB(x) = the longest running time of any halting program of size x This function is not computable, because if we could compute it, we would have solved the halting problem. However, I'm sure it can be defined in a formal language, if we settled on the programming language the programs are written in and so on. Now suppose we try to use Solomonoff induction on a world governed by the Busy Beaver function. Since the busy beaver function is not computable, there will be no Turing machine that computes it. Since Solomonoff induction only considers turing-machine models, then, it will never find the true model for the world. Suppose instead we have some prior over any model that can be formally defined. If we grant the same computational resources that were to solomonoff induction, then we are able to instantly derive the logical consequences of each possible model. These can be compared to the world as it is to create an updated belief in each model. I can give no convergence proof, but it is at least conceivable that such an AI will determine that its world is in fact produced by the busy beaver function. (I didn't invent BB. See http://en.wikipedia.org/wiki/Busy_beaver) ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=95818715-a78a9b Powered by Listbox: http://www.listbox.com
