In the story Alice in Wonderland, Alice fell down a rabbit hole and suddenly found herself in a strange world called Wonderland. Alice gradually developed knowledge about Wonderland by observing, learning, and reasoning. In this paper we present the system Alice In Wonderland that operates analogously. As a theoretical basis of the system, we define several basic concepts of logic in a generalized setting, including the notions of domain, proof, consistency, soundness, completeness, decidability, and compositionality. We also prove some basic theorems about those generalized notions. Then we model Wonderland as an arbitrary symbolic domain and Alice as a cognitive architecture that learns autonomously by observing random streams of facts from Wonderland. Alice is able to reason by means of computations that use bounded cognitive resources. Moreover, Alice develops her belief set by continuously forming, testing, and revising hypotheses. The system can learn a wide class of symbolic domains and challenge average human problem solvers in such domains as propositional logic and elementary arithmetic.