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

Abstract

AbstractBipolar 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.KeywordsModal LogicAtomic PropositionPossibility DistributionFormal Concept AnalysisPossibility TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.