There is a growing interest for multi-scale agent-based modeling. The research community has made several efforts in proposing agent-based simulators or meta-models, which accommodate for multi-scale agent-based modeling. Unfortunately, the proposed simulators are often tight to a specific model. And the proposed meta-models exist only as formal proposals without a concrete implementation supported by an operational modeling language. The lack of a common operational meta-model and an associated operational modeling language raises the question of reusability and increase the danger of "re-inventing the wheel" when one develops new models. Moreover, the operational semantics of such multi-scale models may differ without having defined a solid theoretical ground. Our research aims at proposing a generic meta-model for multi-scale agent-based modeling. In our approach, we revisit the fundamental notions of agent modeling (agent/environment/scheduler) in order to support a recursive representation of these notions in an agent-based model. To test the operational semantic of the proposed model, we implement this meta-model as an agent-based modeling language in the GAMA simulation platform. This paper presents such a meta- model and how its concepts can be used to formalize multi-scale agent-based models.