Possibilistic logic bases and possibilistic graphs

TL;DR

This paper explores the relationship between possibilistic logic bases and possibilistic graphs, providing translations between the two frameworks and analyzing their semantic equivalence in representing possibility distributions.

Contribution

It introduces methods to translate between possibilistic graphs and bases, and compares two conditioning approaches within possibility theory.

Findings

Semantic equivalence when leading to the same possibility distribution

Translation methods between graphs and bases are established

Two conditioning types induce distinct possibilistic graphs

Abstract

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representations are semantically equivalent when they lead to the same possibility distribution (which rank-orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning which exist in possibility theory (one based on product in a numerical setting, one based on minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. In both cases, a translation of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.