Toward a general theory of conditional beliefs

✍ Scribed by Giulianella Coletti; Romano Scozzafava

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 227 KB
• Volume: 21
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.20133

✦ Synopsis

We consider a class of general decomposable measures of uncertainty, which encompasses ~as its most specific elements, with respect to the properties of the rules of composition! probabilities, and ~as its most general elements! belief functions. The aim, using this general context, is to introduce ~in a direct way! the concept of conditional belief function as a conditional generalized decomposable measure w~{6{!, defined on a set of conditional events. Our main tool will be the following result, that we prove in the first part of the article and which is a sort of converse of a well-known result ~i.e., a belief function is a lower probability!: a coherent conditional lower probability tP~{6K ! extending a coherent probability P~H i !-where the events H i s are a partition of the certain event V and K is the union of some ~possibly all! of them-is a belief function.