Through mathematical theories, models, and experimental computation, Artificial Intelligence with Uncertainty explores the uncertainties of knowledge and intellect that occur during human cognitive processes. The authors focus on the importance of natural-language carrier of knowledge and intelligence-for artificial intelligence (AI) study. This book develops a framework that shows how uncertainty in AI expands and generalizes traditional AI. In addition, the present inverted pendulum example to discuss reasoning and control with a sure knowledge of physics and provides a cognitive model to visualize human thinking with hierarchy. With in-depth discussion about the basics, methodology, and uncertainty in AI, this book explains and simulates human thought, leading to a better understanding of cognitive processes.