Emergence is the kernel concept of complexity science. Lack of precision when people refer to “emergent properties” hinders the research of complex systems. The purpose of this paper is to develop a formal definition of emergence to make it intrinsic to a system and to integrate different views on emergence.
Based on the modeling framework of entity grammar systems (EGS), a formal definition of emergence is proposed and a theorem is obtained for exploring the producing conditions of emergence. With the definition and theorem, three views on emergence are unified using the same formalism of EGS.
The concept of emergence can be formally defined in the framework of EGS to integrate the “downward causation” and “upward causation” views of emergence and makes emergent properties intrinsic to a system. It is possible to control the production of emergence when the system is analyzed using the formalism of EGS.
A formal definition of emergence is proposed in this paper. This work combines the modeling power of EGS with the formal analysis of emergence, which will prompt the further application of EGS in modeling, simulation, and analysis of complex systems in many fields and will provide practical tools for complexity research.
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