Modeling positive and negative information in possibility theory

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Journal Article
International Journal of Intelligent Systems, 2008, 23 (10), pp. 1094 - 1118
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From a knowledge representation point of view, it may be interesting to distinguish between (i) what is potentially possible because it is not inconsistent with the available knowledge on the one hand, and (ii) what is actually possible because it is reported from observations on the other hand. Such a distinction also makes sense when expressing preferences, to point out positively desired choices among merely tolerated ones. Possibility theory provides a representation framework where this distinction can be made in a graded way. The two types of information can be encoded by two types of constraints expressed in terms of necessity measures and in terms of so-called 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, where clauses (resp., phrases) are weighted in terms of a necessity measure (resp., a guaranteed possibility function). By application of a minimal commitment principle, the two bases induce a pair of possibility distributions at the semantic level, for which a consistency condition should hold to ensure that what is claimed to be actually possible is indeed not impossible. 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, as well as in the representation of "if-then" rules in terms of examples and counterexamples. © 2008 Wiley Periodicals, Inc.
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