Abram, I agree with the spirit of your post, and I even go further to include "being open" in my working definition of intelligence --- see http://nars.wang.googlepages.com/wang.logic_intelligence.pdf
I also agree with your comment on Solomonoff induction and Bayesian prior. However, I talk about "open system", not "open model", because I think model-theoretic semantics is the wrong theory to be used here --- see http://nars.wang.googlepages.com/wang.semantics.pdf Pei On Thu, Sep 4, 2008 at 2:19 PM, Abram Demski <[EMAIL PROTECTED]> wrote: > 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/?&; > 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
