Abstract. We present the system O that operates in arbitrary symbolic domains, including arithmetic, logic, and grammar. O can start from scratch and learn the general laws of a domain from examples. The main learning mechanism is a formalization of Occam's razor. Learning is facilitated by working within a cognitive model of bounded rationality. Computational complexity is thereby dramatically reduced, while preserving human-level performance. As illustration, we describe the learning process by which O learns elementary arithmetic. In the beginning, O knows nothing about the syntax or laws of arithmetic; by the end, it has constructed a theory enabling it to solve previously unseen problems such as "what is 67 * 8?" and "which number comes next in the sequence 8, 11, 14?"
