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

Didier Dubois (1, 2) , Emiliano Lorini (3, 2) , Henri Prade (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 IRIT-LILaC - Logique, Interaction, Langue et Calcul

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.

Mots clés: Data Mining and Knowledge Discovery

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

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, ⟨10.1007/978-3-642-40381-1_16⟩. ⟨hal-01212923⟩