Information Fusion and Revision in Qualitative and Quantitative Settings

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Abstract

Fusion and revision are two key topics in knowledge representation and uncertainty theories. However, various formal axiomatisations of these notions were proposed inside specific settings, like logic, probability theory, possibility theory, kappa functions, belief functions and imprecise probability. For instance, the revision rule in probability theory is Jeffrey’s rule, and is characterized by two axioms. The AGM axioms for revision are stated in the propositional logic setting. But there is no bridge between these axiomatizations. Likewise, Dempster rule of combination was axiomatized by Smets among others, and a logical syntax-independent axiomatization for merging was independently proposed by Koniezny and Pino-Perez, while a belief function can be viewed as a weighted belief set. Moreover the distinction between fusion and revision is not always so clear and comparing sets of postulates for each of them can be enlightening. This paper presents a tentative set of basic principles for revision and another set of principles for fusion that could be valid regardless of whether information is represented qualitatively or quantitatively. In short, while revision obeys a success postulate and a minimal change principle, fusion is essentially symmetric, and obeys a principle of optimism, that tries to take advantage of all sources of information. Moreover, when two pieces of information are consistent, revising one by the other comes down to merging them symmetrically. Finally, there is a principle of minimal commitment at work in all settings, and common to the two operations.