Dalal's revision without hamming distance

Abstract

A well known strategy for belief revision is the use of an operator which takes as input a belief base and formula and outputs a new consistent revised belief base. Many operators require additional information such as epistemic entrenchment relations, system of spheres, faithful orderings, subformulae relation, etc. However, in many applications this extra information does not exist and all beliefs have to be equally considered. Other operators that can do without background information are dependent on the syntax. Among the few operators that possess both kinds of independence: of extra information and of the syntax, Dalal's operator is the most outstanding. Dalal's revision moves from the models of the base to the models of the input formula which are closest in terms of Hamming distance. A drawback of Dalal's approach is that it fails when faced with inconsistent belief bases. This paper proposes a new method for computing Dalal's revision that avoids the computation of belief bases models. We propose a new distance between formulae based on distances between terms of formulae in DNF and a revision operator based on these distances. The proposed operator produces Dalal's equivalent results when the belief base and new input are both consistent. Moreover, this new operator is able to handle inconsistent belief bases. We also analyze several properties of the new operator. While the input belief base and formula need a compilation to DNF, the operator meets desirable properties making the approach suitable for implementation. © Springer-Verlag 2013.