Inference with Idempotent Valuations

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out computations with both representations in an efficient way. The particular cases of finite sets and convex polytopes are considered. 1 INTRODUCTION Valuation Based Systems (VBS) were introduced by Shafer and Shenoy (Shafer and Shenoy 1988, Shafer 1991). This abstract framework to represent and calculate with valuations has been applied to different formalisms, such as Probability, Belief Functions (Shenoy and Shafer 1990), Convex Sets of Probabilities (Cano, Moral and Verdegay L'opez 1993), Possibility Theory (Shenoy 1992), or Propositional Information Systems (Kohlas and Moral 1996). In this paper, we study Valuation Based Systems in which an ..