On Friday 24 November 2006 10:26, William Pearson wrote: > On 24/11/06, J. Storrs Hall, PhD. <[EMAIL PROTECTED]> wrote: > > The open questions are representation -- I'm leaning towards >CSG > > Constructive solid geometry? You could probably go quite far towards a > real world navigator with this, but I'm not usre how you plan to get > it to represent the internal state of other systems, so it can try to > predict what actions people may take due to their emotions etc. I'm in > favour of multiple and changeable representations myself. Quite how to > integrate them all into a somewhat coherent world view is an > interesting problem though.
Imagine a space in which a frame is a single point. This is standard practice in physical science, where the space is sometimes referred to as a "phase space." As the frame evolves in time, it will describe a trajectory in the space. Similar, slightly variant frames will occur near the original one in the space. Combining all possible trajectories under a given constraint produces a subspace that is a hypersurface in the original one, like the "potential energy surfaces" seen in physics and chemistry. (The spaces typically have numbers of dimensions ranging from thousands to Avagadro's number...) A frame can be thought of a sentence, a constraint on the set of possible worlds. The surface can be thought of as a space of possible worlds, and regions in the space represent sentences. Doing CSG on regions in the space is semantically equivalent to using propositional connectives on sentences -- AND = intersection, OR = union, etc. The reason for going to all this trouble is that not only propositional logic, but many other useful conceptual operations have fairly simple geometric cognates in this representation. Conceptual blending is just interpolation. Various kinds of prediction are extrapolation. Some fairly standard forms of metaphor reduce to geometric quadrature: if A is to B as C is to D, A = B + C - D. Finding abstractions reduces to projective geometry, or rather doing abstraction does -- finding useful ones is really the holy grail! The really cool thing about n-spaces as a representation scheme is that they do ground out in simple geometric representations of the physical world at the concrete end, but extend more or less seamlessly into the abstract. Some intermediates: from the 3-d representation of a robot's surroundings, to the n-DOF configuration space of its possible positions, to one with it and all the other objects around, to a Lagrangian space for dynamics where least-energy action planning turns into path-finding. Now take 10 million or so associative memories (think cortical columns), each of which records trajectories of a different frame-type. Most of these are abstractions that are defined in terms of transformations and combinations of other frames, of course. Each one can be used as a CBR-style predictor, planner, and modeller. Hook them all together and you have a fair dinkum engine of reason and seat of the soul. Josh ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
