Coherence Checking and Propagation of Lower Probability Bounds

In this paper we use imprecise probabilities, based on a concept of generalized coherence (g-coherence), for the management of uncertain knowl- edge and vague information. We face the problem of reducing the computational difficulties in g-coherence checking and propagation of lower conditional probabil- ity bounds. We examine a procedure, based on linear systems with a reduced number of unknowns, for the checking of g-coherence. We propose an iterative algo- rithm to determine the reduced linear systems. Based on the same ideas, we give an algorithm for the prop- agation of lower probability bounds. We also give some theoretical results that allow, by suitably modifying our algorithms, the g-coherence checking and propagation by working with a reduced set of variables and/or with a reduced set of constraints. Finally, we apply our algo- rithms to some examples.