Bounded revision: two-dimensional belief change between conservative and moderate revision
The paper develops the idea of belief revision as a comparative operation, in the sense that the input proposition is compared with a reference proposition, and what is done to the belief state depends on the relationship between them. The idea has its roots in \textit{J. Cantwell}'s [``On the logic of small changes in hypertheories'', Theoria 63, No. 1--2, 54--89 (1997)] and \textit{E. Fermé} and \textit{H. Rott}'s [``Revision by comparison'', Artif. Intell. 157, No. 1--2, 5--47 (2004; Zbl 1085.03013)]. For example, in the latter publication, if the reference item is more entrenched than the negation of the input, then we revise by the input; if on the other hand it is not, then we carry out a `severe withdrawal' of the reference. Evidently, that operation involves elements of both revision and contraction, so it does not satisfy the AGM postulates for either one alone. Accordingly, in two texts of 2007 that are available on the web though not in print, the author began work on a modified version that is purely revisionary, still non-numerical, and more general in that the reference proposition need not be an element of the belief set. That construction is carried to completion in the paper under review. A central idea is that the reference sentence should not influence the propositional content of the new belief set, but only the strength with which the input is accepted; after revision, it should be marginally more than that of the reference proposition. Semantically, a belief state is modeled by a system of spheres or (equivalently) an entrenchment ordering of formulae. The resulting system satisfies the AGM postulates for one-shot revision and also the Darwiche-Pearl postulates for its iteration. In the limiting cases that the reference proposition is a tautology or a contradiction, it generates the familiar systems known, respectively, as moderate (aka lexicographic) and conservative (aka natural) revision.
scientific article; zbMATH DE number 6038144
scientific article