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Possibilistic Logic

Keywords: possible worlds

Categories: Inference and Reasoning , Knowledge Representation

Author(s): Fl\'avio Corr\^ea da Silva

Possibilistic logics assign degrees of necessity and possibility to sentences, which express the extent to which these sentences are believed to be necessarily or possibly true, respectively. The semantics of possibilistic logics is defined based on a Fuzzy Set of possible worlds, i.e., a set of possible worlds together with a fuzzy membership function that describes the extent to which each possible world belongs to a referential set. Given a sentence a , the necessity measure N(a) expresses the greatest lower bound for the degree of membership of the worlds that support a , and the related possibility measure Π(a) expresses the least upper bound for this degree of membership. Possibilistic logics should not be confused with Fuzzy Logics. Although the concept of fuzzy measures is central to the description of both of them, in possibilistic logics the truth-values of sentences range on true,false only and necessity and possibility measures describe states of belief, whereas in fuzzy logics the truth-values of sentences range on the interval [0,1] and fuzzy measures describe `degrees of trueness'.



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