A sequential reversible belief revision methods based on polynomials

Abstract : This paper deals with iterated belief change and proposes a revision rule that modifies a plausibility ordering of interpretations in such a way that any world where the input observartion 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 lexicographical ordering. This encoding makes it very easy to implement and iterate the revision rule using simple operations on these polynomials. Moreover, polynonomials allow to keep track of the sequence of observations. Lastly, it is shown how to practically 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 refined one can think of, in accordance with darwiche and Pearl’s principles, and thus contrast with the minimal change rule called natural belief revision.