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This book -the first of a two-volume monograph- seeks to unify the hitherto perceived-as-disparate foundations of psychology and artificial intelligence. It does this by replacing their constitutive notions with a novel common one: noemon system. The ensued Theory of Noemon Systems is developed in terms of an interdisciplinary, language- based, axiomatic approach. The first volume details the development of the foundations of the theory and expounds ramifications for cognitive science and AI including novel solutions to the AGI debate and Darwin's mental gap issue, while o?ering the first complete definition of AI. The book concurrently explores the similarities and di?erences between humans and AI/robot systems with respect to the evolution-dependent phenomena of representation, thinking, understanding and communication. The book is an extensive one; because of it's extensiveness and broad ramifications, this book will appeal to scientists working on the interfaces of psychology, AI, philosophy of mind, neuroscience, and the humanities. The complicated and extensive unification of the fields of Artificial Intelligence and psychology is continued in the second volume that breaks further new ground for both disciplines, with thought-provoking and compelling implications for both.