On cognitive informatics foundations of knowledge and formal knowledge systems

Knowledge is acquired information in forms of data, behavior, experience, and skills retained in memory through learning. This paper presents the nature of human knowledge, its mathematical model, and its manipulation by concept algebra. The taxonomy of knowledge and its hierarchical abstraction model of knowledge are investigated. Mathematical models of knowledge and its manipulation by concept algebra are developed. The theory of knowledge acquisition and the cognitive model of knowledge spaces are formally described covering the effort and complexity models of knowledge creation and acquisition. The framework of formalized knowledge systems is developed based on the analyses of formal and empirical knowledge.