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Making Revision Reversible: an Approach Based on Polynomials

Benferhat S., Dubois D., Lagrue S., Papini O.

Fundamenta Informaticae

2002

Vol. 53, nr 3,4

251-280

This paper deals with iterated belief change and proposes a drastic revision rule that modifies a plausibility ordering of interpretations in such a way that any world where the input observation holds is more plausible that any world where it does not. This change rule makes sense in a dynamic context where observations are received, and the newer observations are considered more plausible than older ones. It is shown how to encode an epistemic state using polynomials equipped with the lexicographic ordering. This encoding makes it very easy to implement and iterate the revision rule using simple operations on these polynomials. Moreover, polynomials allow to keep track of the sequence of observations. Lastly, it is shown how to efficiently compute the revision rule at the syntactical level, when the epistemic state is concisely represented by a prioritized belief base. Our revision rule is the most drastic one can think of, in accordance with Darwiche and Pearl's principles, and thus contrasts with the minimal change rule called natural belief revision. The paper also shows how to obtain the reversibility of Boutilier's natural belief revision and possibilistic revision using polynomials.