A novel modelling paradigm for online diagnostics and prognostics for autonomous systems is presented. A model for the autonomous system being diagnosed is designed using a logic-based formalism. The model supports the run-time ability to verify that the autonomous system is safe and reliable for operation within a dynamic environment. The paradigm is based on the philosophy that there are different types of semantic relationships between the states of different parts of the system. A finite state automaton is devised for each sensed component and some of the non-sensed components. To capture the interdependencies of components within such a complex robotic platform, automatons were related to each other by semantic relationships. Modality was utilised by the formalism to abstract the relationships and to add measures for the possibility and uncertainty of the relationships. The complexity of the model was analysed to evaluate its scalability and applicability to other systems. The results demonstrate that the complexity is not linear and a computational time of 10 ms was required to achieve run-time diagnostics for 2200 KB of knowledge for complex system interdependences. The ability to detect and mitigate hardware related failures was demonstrated within a confined space autonomous operation. Our findings provide evidence of the applicability of our approach for the significant challenge of run-time safety compliance and reliability in autonomous systems.