Bipolar Possibilistic Representations

TL;DR

This paper introduces a bipolar possibilistic framework that distinguishes between possible and guaranteed possible values, enhancing knowledge representation, preference modeling, and diagnostic reasoning within possibility theory.

Contribution

It formalizes a bipolar possibilistic approach using necessity measures and guaranteed possibility functions, including conditional and context-dependent constraints.

Findings

Provides a formal semantic framework for bipolar possibilistic representations.

Extends possibilistic models to include guaranteed possibilities and conditional measures.

Highlights applications in preferences and diagnostic knowledge representation.

Abstract

Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be useful when representing knowledge, for modelling values which are not impossible because they are consistent with the available knowledge on the one hand, and values guaranteed to be possible because reported from observations on the other hand. It is also of interest when expressing preferences, to point out values which are positively desired among those which are not rejected. This distinction can be encoded by two types of constraints expressed in terms of necessity measures and in terms of guaranteed possibility functions, which induce a pair of possibility distributions at the semantic level. A consistency condition should ensure that what is claimed to be guaranteed as possible is indeed not impossible. The present paper investigates the representation of this bipolar view, including the case when it is stated by means of conditional measures, or by means of comparative context-dependent constraints. The interest of this bipolar framework, which has been recently stressed for expressing preferences, is also pointed out in the representation of diagnostic knowledge.