Smart systems equipped with emerging pervasive computing technologies enable people with limitations to live in their homes independently. However, lack of guarantees for correctness prevent such system to be widely used. Analysing the system with regard to correctness requirements is a challenging task due to the complexity of the system and its various unpredictable faults. In this work, we propose to use formal methods to analyse pervasive computing (PvC) systems. Firstly, a formal modelling framework is proposed to cover the main characteristics of such systems (e.g., context-awareness, concurrent communications, layered architectures). Secondly, we identify the safety requirements (e.g., free of deadlocks and conflicts) and specify them as safety and liveness properties. Furthermore, based on the modelling framework, we propose an approach of verifying reasoning rules which are used in the middleware for perceiving the environment and making adaptation decisions. Finally, we demonstrate our ideas using a case study of a smart healthcare system. Experimental results show the usefulness of our approach in exploring system behaviours and revealing system design flaws such as information inconsistency and conflicting reminder services.