Bipolar Possibility Theory as a Basis for a Logic of Desire and Beliefs

Abstract : Bipolar possibility theory relies on the use of four set functions. On the one hand, a weak possibility and a strong necessity measure are increasing set functions, which are respectively max-decomposable with respect to union and min-decomposable with respect to intersection. On the other hand, strong possibility and weak necessity measures are two decreasing set functions, which are respectively min-decomposable with respect to union and max-decomposable with respect to intersection. In the first part of the paper we advocate the use of the last two functions for modeling a notion of graded desire. Moreover, we show that the combination of weak possibility and strong possibility allows us to model a notion of realistic desire, i.e., a desire that does not only account for satisfactoriness but also for its epistemic possibility. In the second part of the paper we show that possibility theory offers a semantic basis for developing a modal logic of beliefs and desires.
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Didier Dubois, Emiliano Lorini, Henri Prade. Bipolar Possibility Theory as a Basis for a Logic of Desire and Beliefs. 7th International Conference on Scalable Uncertainty Management (SUM 2013), Sep 2013, Washington, DC, United States. pp. 204-218. ⟨hal-01212923⟩

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