Object-oriented methodology is widely used in the information system development field. Nonetheless, recent research studies have discovered that the modelling grammars that use object-oriented methodology lack necessary constructs to represent certain real-world semantics. Therefore, the use of such grammars with their shortcomings can produce defective conceptual models, thereby producing defective information systems. Evermann and Wand (2005, 2009) studied this issue and proposed a set of rules for object-oriented grammatical constructs to represent static and behaviour semantics of a real-world phenomenon. This paper extends their work by proposing object-oriented grammatical rules for the interactional and external environmental semantics of a real-world phenomenon. This representation is exemplified using an object-oriented modelling grammar namely Unified Modelling Language (UML). Subsequently, the set of new rules has been validated using a case study. This extended UML facilitates seamless integration between the conceptual model and its system model.