In a closed model, every statement is either true or false. In an open model, every statement is either true or uncertain. In reality, all statements are uncertain, but we have a means to assign them probabilities (not necessarily accurate probabilities).
A closed model is unrealistic, but an open model is even more unrealistic because you lack a means of assigning likelihoods to statements like "the sun will rise tomorrow" or "the world will end tomorrow". You absolutely must have a means of guessing probabilities to do anything at all in the real world. -- Matt Mahoney, [EMAIL PROTECTED] --- On Thu, 9/4/08, Abram Demski <[EMAIL PROTECTED]> wrote: > From: Abram Demski <[EMAIL PROTECTED]> > Subject: [agi] open models, closed models, priors > To: agi@v2.listbox.com > Date: Thursday, September 4, 2008, 2:19 PM > A closed model is one that is interpreted as representing > all truths > about that which is modeled. An open model is instead > interpreted as > making a specific set of assertions, and leaving the rest > undecided. > Formally, we might say that a closed model is interpreted > to include > all of the truths, so that any other statements are false. > This is > also known as the closed-world assumption. > > A typical example of an open model is a set of statements > in predicate > logic. This could be changed to a closed model simply by > applying the > closed-world assumption. A possibly more typical example of > a > closed-world model is a computer program that outputs the > data so far > (and predicts specific future output), as in Solomonoff > induction. > > These two types of model are very different! One important > difference > is that we can simply *add* to an open model if we need to > account for > new data, while we must always *modify* a closed model if > we want to > account for more information. > > The key difference I want to ask about here is: a > length-based > bayesian prior seems to apply well to closed models, but > not so well > to open models. > > First, such priors are generally supposed to apply to > entire joint > states; in other words, probability theory itself (and in > particular > bayesian learning) is built with an assumption of an > underlying space > of closed models, not open ones. > > Second, an open model always has room for additional stuff > somewhere > else in the universe, unobserved by the agent. This > suggests that, > made probabilistic, open models would generally predict > universes with > infinite description length. Whatever information was > known, there > would be an infinite number of chances for other unknown > things to be > out there; so it seems as if the probability of *something* > more being > there would converge to 1. (This is not, however, > mathematically > necessary.) If so, then taking that other thing into > account, the same > argument would still suggest something *else* was out > there, and so > on; in other words, a probabilistic open-model-learner > would seem to > predict a universe with an infinite description length. > This does not > make it easy to apply the description length principle. > > I am not arguing that open models are a necessity for AI, > but I am > curious if anyone has ideas of how to handle this. I know > that Pei > Wang suggests abandoning standard probability in order to > learn open > models, for example. > > --Abram Demski > ------------------------------------------- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
