Intention, a crucial part of the mental states of an agent, plays an important role in determining the behaviors of the rational agent. In order to eliminate the flaws with existing logic of intention and establish a suitable semantic representation for intention, this paper addresses the requests for intention semantics on formal frameworks of rational agents, points out the problems with existing logic of intention, introduces a novel possible world semantics for intention, called the improved twin-subset semantics, which was developed by us recently based on the previous work about the true-false subset semantics, and presents its application in the formalization of intention for agent. It is also proved that some desired properties could be obtained through some restrictions to the algebraic structure of the models. In the two-value logic, the false value is as important as the true value. Of course, to one proposition, once the true values are described in some possible worlds, the false values are just the rest. However, to a set of propositions (the agent intents to do), descriptions to the false values are as important as descriptions to the true values. The representation of intention should describe a set of propositions (the propositions agent intents to achieve), but in the possible world semantics of classical normal modal operator, it merely pays attention to the true-value, which is denoted as R_I(w), and can be considered as single-subset semantics. In the improved twin-subset semantics, the false-value is considered as important as the true-value, and R_IT(w) is used to describe the true, while R_IF(w) the false. Thus this method can describe modal operator in two-value logic completely. In addition, the possible world semantics of the classical normal modal operator can be regarded as the degradation of the improved twin-subset semantics when R_IF(w)=?. It not only avoids the logical omniscience problem and other related problems (such as side-effect problem, and etc) but also overcomes the shortcomings of the true-false subset semantics and twin-subset semantics. Compared with Konolige and Pollack’s model of intention, this model not only is simpler and more natural, but also satisfies the K-axiom and the Joint Consistency. Actually, the improved twin-subset semantics provides a new method for semantic representation of non-normal modal operator and can be applied to establish a new proper agent’s logic system.