Formal frameworks for the specification of rational agents are commonly based on logic of belief, desire and intention. In order to eliminate the problems with existing logic of belief, desire and intention, and to provide a proper semantic representation for non-normal modal operator, the problems with existing logic of belief, desire and intention are addressed, the true-false subset semantics, which is developed by the authors, and its application in the formalization of agent are introduced. The propose framework invalidates the problematic properties of intention, and by imposing certain constraints on the algebraic structure of the models, it is showed that many desirable properties can be obtained. Finally the true-false subset semantics is analyzed. Thus the true-false subset semantics provides a proper semantic representation for non-normal modal operator. It is an important development of classical possible worlds semantics for non-normal modal operator. It is an important development of classical possible worlds semantics for normal modal operators, and is proved to be a powerful tool for the logical specification of rational agent behavior. It can be applied to establish a new proper agent logic system.