The is-a relationship among actors has been introduced since the very beginning of i*. However, the effect of this construct at the level of intentional elements and dependencies is not always clear. In this paper, we explore the semantics of inheritance in i*. Aligning with its usual meaning in object-orientation, we distinguish 3 main notions to be defined: extension, refinement, and redefinition. For each of them, we study its effects on the different types of intentional elements and their links, and also dependencies, making explicit what can be and cannot be done. We illustrate the proposal with an example that makes intensive use of inheritance, a multi-stakeholder distributed system in which different types of related stakeholders co-exist.