When Alice in Wonderland fell down the rabbit hole, she entered a world that was completely new to her. She gradually explored that world by observing, learning, and reasoning. This paper presents a simple system ALICE IN WONDERLAND that operates analogously. We model Alice’s Wonderland via a general notion of domain and Alice herself with a computational model including an evolving belief set along with mechanisms for observing, learning, and reasoning. The system operates autonomously, learning from arbitrary streams of facts from symbolic domains such as English grammar, propositional logic, and simple arithmetic. The main conclusion of the paper is that bounded cognitive resources can be exploited systematically in artificial general intelligence for constructing general systems that tackle the combinatorial explosion problem and operate in arbitrary symbolic domains.