Whilst narrative representations have played a prominent role in AI research, there has been a renewed interest in the topic with the development of interactive narratives. A typical approach aims at generating narratives from baseline action representations, most often using planning techniques. However, this research has developed empirically, often as an application of planning. In this paper, we explore a more rigorous formalisation of narrative concepts, both at the action level and at the plot level. Our aim is to investigate how to bridge the gap between action descriptions and narrative concepts, by considering the latter from the perspective of resource consumption and causality. We propose to use Linear Logic, often introduced as a logic of resources, for it provides, through linear implication, a better description of causality than in Classical and Intuitionistic Logic. Besides advances in the fundamental principles of narrative formalisation, this approach can support the formal validation of scenario description as a preliminary step to their implementation via other computational formalisms.