Linköping University Electronic Press:    Electronic Articles in Computer and Information Science

Modeling positive and negative information in possibility theory

Title:Modeling positive and negative information in possibility theory
Authors: Salem Benferhat, Didier Dubois, Souhila Kaci, and Henri Prade
Series:Linköping Electronic Articles in Computer and Information Science
ISSN 1401-9841
Issue:Vol. 7 (2002): no 017

Abstract: From a representation point of view, it may be interesting to distinguish between i) what is possible because it is consistent with the available knowledge on the one hand, and ii) what is guaranteed to be possible because it is reported from observations on the other hand. Such a distinction also makes sense when expressing preferences, in order to point out choices which are positively desired among those which are not rejected. Possibility theory provides a representation framework where this distinction can be made in a graded way. In logical terms, the two types of information can be encoded by two types of constraints expressed in terms of necessity measures and in terms of guaranteed possibility functions. These two set functions are min-decomposable with respect to conjunction and disjunction respectively. This gives birth to two forms of possibilistic logic bases, which can viewed as generalized CNF and DNF respectively. By application of a minimal commitment principle, they induce a pair of possibility distributions at the semantic level, for which a consistency condition should hold in order to ensure that what is claimed to be guaranteed as possible is indeed not impossible. The bilattice structure underlying the framework is pointed out. The paper provides a survey of this bipolar representation framework, including the use of conditional measures, or the handling of comparative context-dependent constraints. The interest of the framework is stressed for expressing preferences, or in the representation of if then rules in terms of examples and counter-examples.

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