Pei, I sympathize with your care in wording, because I'm very aware of the strange meaning that the word "model" takes on in formal accounts of semantics. While a cognitive scientist might talk about a person's "model of the world", a logician would say that the world is "a model of a first-order theory". I do want to avoid the second meaning. But, I don't think I could fare well by saying "system" instead, because the models are only a part of the larger system... so I'm not sure there is a word that is both neutral and sufficiently meaningful.
Do you think it is impossible to apply probability to open models/theories/systems, or merely undesirable? On Thu, Sep 4, 2008 at 8:10 PM, Pei Wang <[EMAIL PROTECTED]> wrote: > 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/?&; > 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
