Agent-based models have been used for diverse domains such as military, sociology, and urban planning. There is a growing concern about the incrementality and the flexibility of the agent-based models in further sophisticated and large-scale utilization. To resolve this concern, we suggest that specifying agent-based models formally will resolve the problems of incrementality and flexibility of the agent-based models through an organized composition of model components. To organize the composition of agent-based models, we survey formalisms that are applicable to agent-based models, including formalisms from the discrete event models, i.e., DEVS, MDEVS, and Cell-DEVS, as well as formalisms used in the communities of agent-based models, i.e., BDI, MDP, and Game Theory. Then, we compare, contrast, and propose an overarching formal specification for agent-based models that embody the key nature of agents. As an example, we show how to incrementally merge and flexibly manage traditional agent-based models through proposed formal specifications.