Having the formal definitions of emotional states allows us to show how, and why, emotions may be useful to a rational agent. First, by modifying the decision-theoretic model used for deliberative rationality, emotions allow the agent to control the allocation of its cognitive resources and the complexity of its deliberations under time pressure in an uncertain environment. For example, limiting the number of alternative behaviors considered, or shortening the time horizon of these alternatives allows for more rapid decision-making.
Second, emotions and feelings turn out to be valuable when the agent finds it useful to inform other agent(s) about its own internal state. Instead of having to describe the details of its internal state, and running the risk of being misunderstood if the other agents are engineered differently, the agent can use more abstract and universal terms. For example, notions of stress or panic may be convenient to express the fact that the urgency of the situation forced the agent to look at only short-term effects of its actions. Thus, in the context of communication with other agents, the formal definitions of emotions serve as semantics of emotional terms, with which the agents can express their own internal states and understand the states the other agents are in.
Third, well-defined emotional states of self and others are crucial in the agent's interaction with humans. Frequently, human-computer interaction is impeded by the machine being hopelessly out-of-step with the emotional state of the human user. It turns out, however, that the users' emotional state can be assessed using measurable and inferred factors, and it is important for the machine to model the effect the user's emotional state has on the user's decision-making and his/her tendency to action.