On the transformation between possibilistic logic bases and possibilistic causal networks

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former ranks 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 representation 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 that exist in possibility theory (one based on the product in a numerical setting, one based on the minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. This article deals with the links between the logical and the graphical frameworks in both numerical and quantitative settings. 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. 2002 Elsevier Science Inc. All rights reserved. International Journal of Approximate Reasoning 29 (2002) 135–173 www.elsevier.com/locate/ijar This paper is a fully revised and extended version of two conference papers [6,7]. * Corresponding author. E-mail addresses: [email protected] (S. Benferhat), [email protected] (D. Dubois), [email protected] (L. Garcia), [email protected] (H. Prade). 0888-613X/02/$ see front matter 2002 Elsevier Science Inc. All rights reserved. PII: S 0 8 8 8 6 1 3 X ( 0 1 ) 0 0 0 6 1 5