Since business rules aim at enforcing regulations in an organization, they are critical in governing business activities from a managerial standpoint. On the other hand, another type of rules has emerged in context-aware service systems: context rules. Context rules are employed for context reasoning to recommend and operate the right services in an appropriate manner. In this sense, context rules ensure the smartness of services in smart service systems. For decades, researchers and practitioners have addressed rule modelling and rule management in information systems and business services. However, in relation to context-aware services in smart service systems, there is a lack of exploring the rule aspect, especially considering how business rules and context rules are involved in such a system. The purpose of this paper is to propose a rule modelling framework (called RuCBS framework) for expressing rules in context-aware smart service systems over the three aspects of service science (Management, Science, and Engineering). The framework presents concepts, a meta-model that connects these concepts, and rule patterns. The framework is validated with a case study on banking services. Future research directions on rules in context-aware smart service systems are also discussed.