<p>An aircraft is composed of several complicated systems interacting with each other at different levels to ensure safe flight. Faults originating from one airborne system may propagate to others, potentially leading to a series of faults and even severe consequences. To enhance flight safety, minimize false alarms and reduce maintenance costs, it is essential to develop efficient and precise fault diagnosis techniques. This paper investigates the theory and methodology of multiple fault diagnosis in airborne systems. Fault diagnosis logic equations are adopted to model the cause-effect relationship between fault modes and fault symptoms. In addition, the existence of solutions to fault diagnosis logic equations is theoretically proved. Fault diagnosis logic equations may have a unique solution, more than one solution or no solutions under different conditions. Regarding the problem that fault diagnosis logic equations may have more than one solution or no solutions, an algorithm for solving fault diagnosis logic equations is proposed. The algorithm ensures that, for any given combination of fault symptoms, fault diagnosis logic equations will have a unique solution, enabling precise fault reasoning and isolation. Finally, a case study is carried out to verify the proposed method and results demonstrate that fault diagnosis logic equations-based approach achieves high diagnostic accuracy.</p>