The geometry of knowledge acquisition through motion and sensing

In order to understand knowledge acquisition in autonomous systems, we introduce a representational framework in which knowledge about the world is represented as a point in a knowledge space. This is a homogeneous linear space, with an unusual vector product (the componentwise multiplication of vectors). We demonstrate how motions in the world lead to an induced linear transformation on the knowledge space, and how sensing leads to an induced reduction to a linear subspace. We also investigate how abstraction and reasoning, which are internal transformations of the knowledge, may be represented in the knowledge space. We treat applications of the framework which demonstrate how it can be combined with Bayesian decision theory to compute optimal goal-directed behavior for both discrete and continuous cases.