Detecting Emergent Behaviors with Semi-Boolean Algebra

Aerospace and military systems are becoming increasingly interconnected. In turn, their collective behavior is more difficult to predict. The emergent properties of systems of systems make them powerful, but also more difficult to design, assure proper behavior, operate correctly, and ensure they have no new security holes. Learning and adaptation causes additional concerns. Emergent behavior patterns cannot be fully predicted through the use of traditional system development methods, including testing and model checking. In addition, self-organization can occur as individual systems optimize to address inefficiencies in the larger system. Designing for and detecting emergent behavior has not been addressed in current systems development methodologies. This paper gives background on approaches for modeling and verifying emergent behavior and discusses the use of semi-Boolean algebra as a means for detecting emergence in combined behaviors. Semi-Boolean algebra is a generalization of the Boolean algebra by weakening the requirement that any two elements have a common upper bound. The paper also shares an example approach for modeling and verifying emergent behavior and describes several ways to detect emergent behavior with this technique.