Possibilistic networks are graphical models that compactly encode joint possibility distributions. This paper studies a new form of possibilistic graphical models called three-valued possibilistic networks. Contrary to standard belief networks where the beliefs are encoded using belief degrees within the interval, three-valued possibilistic networks only allow three values: 0, 1 and {0, 1}. The first part of this paper addresses foundational issues of three-valued possibilistic networks. In particular, we show that the semantics that can be associated with a three-valued possibilistic network is a family of compatible boolean networks. The second part of the paper deals with inference issues where we propose an extension to the min-based chain rule for three-valued networks. Then, we show that the well-known junction tree algorithm can be directly adapted for the three-valued possibilistic setting.
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