On Abstract Systems and System Algebra

Systems are the most complicated entities and phenomena in the physical, information, and social worlds across all science and engineering disciplines. This paper presents a mathematical theory of system algebra and its applications in cognitive informatics, system engineering, and software engineering. A rigorous treatment of abstract systems is described, and the algebraic relations and operations of abstract systems are analyzed. Important properties of systems such as system mutation, work done by systems, the maximum output of systems, system equilibriums, system synchronization, and system dissimilation, are formally modeled. An age-long myth in system theory that states ´the whole is larger than the sum of its parts´ is formally explained. On the basis of the abstract system theory, a wide range of real world phenomena and problems can be explained and solved