A cognitive knowledge base (CKB) is a novel structure of intelligent knowledge base that represents and manipulates knowledge as a dynamic concept network mimicking human knowledge processing. The essence of CKB is the denotational mathematical model of formal concept that is dynamically associated to other concepts in a CKB beyond conventional rule-based or ontology-based knowledge bases. This paper presents a formal CKB and autonomous knowledge manipulation system based on recent advances in neuroinformatics, concept algebra, semantic algebra, and cognitive computing. An item knowledge in CKB is represented by a formal concept, while the entire knowledge base is embodied by a dynamic concept network. The CKB system is manipulated by algorithms of knowledge acquisition and retrieval on the basis of concept algebra. CKB serves as a kernel of cognitive learning engines for cognitive robots and machine learning systems. CKB plays a central role not only in explaining the mechanisms of human knowledge acquisition and learning, but also in the development of cognitive robots, cognitive learning engines, and knowledge-based systems.