Thursday, February 20, 2003, 10:58:57 AM, Ben Goertzel wrote:
BG> OK... I can see that I formulated the problem too formally for a lot of BG> people BG> I will now rephrase it in the context of a specific "test problem." <snip> BG> I don't know if this "test problem" will clarify things or confuse them ;-) For me, it's confused them. I thought I was following it before, sorta...Maybe you're leaving out some initial assumptions, or maybe Shane can clarify. BG> Consider the unit square in the plane, i.e. a square of area 1. BG> Consider n rectangles inside the unit square. Call these rectangles X_1, BG> X_2,..., X_n Are these rectangles at arbitrary locations or all with their origin at the unit square's origin? BG> Now, we may define some probabilities: BG> P(X_i) = the area of the rectangle X_i BG> P(X_i | X_j) = (the area of the intersection between the rectangle X_i and BG> the rectangle X_j) / (the area of the rectangle X_j) So P(X_i | X_j) = how much (from 0 to 1) of X_j is covered by X_i, right? BG> Conceptually, if you like, you can think of the set of rectangles as a Venn BG> diagram, so that the points in the unit square are things in the world, and BG> each X_i represents some concept (defined extensionally as a set of things) BG> Now the test problem is as follows. BG> 1) Choose a large number of points in the unit square BG> 2) Based on these points, evaluate *some of* the probabilities P(X_i) and BG> P(X_i | X_j) I don't understand how we get this from the points...are we getting approximations by selecting arbitrary points and finding out how many hit X_i and X_j? Or do we select a point (x,y) and get some information back? BG> 3) Provide an AI system with no information other than the probabilities BG> evaluated in step 2 BG> 4) Ask the AI system to evaluate the rest of the probabilities P(X_i) and BG> P(X_i | X_j) BG> This is an actual test problem we've used to tweak parameters of Novamente's BG> first-order inference module (which embodies one solution to the problem)... Do we know n (how many rectangles total)? Are there some other relationships involved between these rectangles? All I'm getting out of this is "we know some rectangles in the unit square, we know some overlaps, now figure out the rest" but I can't see how what constrains "the rest" from being completely arbitrary in the given scenario. Maybe I need more math and/or coffee, but I think something's being left out... -- Cliff ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
