In intentional agents, actions are derived from the mental attitudes and their relationships. In particular, preferences (positive desires) and restrictions (negative desires) are important proactive attitudes which guide agents to intentions and eventually to actions. In this paper, we present a general logical framework to represent and reasoning about gradual notions of desires and intentions, including sound and complete axiomatizations. Some extensions are proposed corresponding to certain additional constraints that the agent can set about the kind of preferences she is dealing with. We also show that the framework is expressive enough to describe how desires, together with other information, can lead agents to intentions.
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