Cognitive robots are brain-inspired robots that are capable of inference, perception, and learning mimicking the cognitive mechanisms of the brain. Cognitive learning theories and methodologies for knowledge and behavior acquisition are centric in cognitive robotics. This paper explores the cognitive foundations and denotational mathematical means of cognitive learning engines (CLE) and cognitive knowledge bases (CKB) for cognitive robots. The architectures and functions of CLE are formally presented. A content-addressed knowledge base access methodology for CKB is rigorously elaborated. The CLE and CKB methodologies are not only designed to explain the mechanisms of human knowledge acquisition and learning, but also applied in the development of cognitive robots, cognitive computers, and knowledge-based systems.