This paper aims to introduce a new representation framework of cognitive state of agents, which includes depictions for intention, belief, and goal, and supplies a necessary theoretical basis for constructing agent architecture. In this formalization, all intentions for a goal form a structure with two orders, one represents the temporal order and the other represents the relevant relations among intentions. At the same time, this paper investigates the relationships among beliefs, intentions, and goals. Since this framework gets rid of modal operators to depict intention, intention base, temporal and relevant relation are be adopted to represent intention when agents are constructed, which can narrow the gap between the agent model and agent architecture.