How to Extend the Abstraction Refinement Model for Systems with Emergent Behavior ?

The Abstraction Refinement Model has been widely adopted since it was firstly proposed many decades ago. This powerful model of software evolution process brings important properties into the system under development, properties such as the guarantee that no extra behavior (specifically harmful behaviors) will be observed once the system is deployed. However, perfect systems with such a guarantee are not a common thing to find in real world cases, anomalies and unspecified behaviors will always find a way to manifest in our systems, behaviors that are addressed in this paper with the name "emergent behavior". In this paper, we extend the Abstract Refinement Model to include the concept of the emergent behavior. Eventually, this should enable system developers to: (i) Concretely define what an emergent behavior is, (ii) help reason about the potential sources of the emergent behavior along the development process, which in return will help in controlling the emergent behavior at early steps of the development process.