Belief Change based on Knowledge Measures

Abstract

Knowledge Measures (KMs) aim at quantifying the amount of knowledge/information that a knowledge base carries. On the other hand, Belief Change (BC) is the process of changing beliefs (in our case, in terms of contraction, expansion and revision) taking into account a new piece of knowledge, which possibly may be in contradiction with the current belief. We propose a new quantitative BC framework that is based on KMs by defining belief change operators that try to minimise, from an information-theoretic point of view, the surprise that the changed belief carries. To this end, we introduce the principle of minimal surprise. In particular, our contributions are (i) a general information-theoretic approach to KMs for which [1] is a special case; (ii) KM-based BC operators that satisfy the so-called AGM postulates; and (iii) a characterisation of any BC operator that satisfies the AGM postulates as a KM-based BC operator, i.e., any BC operator satisfying the AGM postulates can be encoded within our quantitative BC framework. We also introduce quantitative measures that account for the information loss of contraction, information gain of expansion and information change of revision. We also give a succinct look into the problem of iterated revision, which deals with the application of a sequence of revision operations in our framework, and also illustrate how one may build from our KM-based contraction operator also one not satisfying the (in)famous recovery postulate, by focusing on the so-called severe withdrawal model as an illustrative example.