Surprise Minimization Revision Operators

TL;DR

This paper introduces a new measure of surprise called relative surprise for belief revision, which considers the broader context of new information and extends existing models by characterizing surprise minimization operators.

Contribution

It proposes a novel relative surprise measure and characterizes the associated revision operator using rationality postulates, extending belief revision theory.

Findings

Introduces the relative surprise measure based on distance notions.

Provides representation results for existing revision operators.

Extends belief revision models with a context-aware surprise measure.

Abstract

Prominent approaches to belief revision prescribe the adoption of a new belief that is as close as possible to the prior belief, in a process that, even in the standard case, can be described as attempting to minimize surprise. Here we extend the existing model by proposing a measure of surprise, dubbed relative surprise, in which surprise is computed with respect not just to the prior belief, but also to the broader context provided by the new information, using a measure derived from familiar distance notions between truth-value assignments. We characterize the surprise minimization revision operator thus defined using a set of intuitive rationality postulates in the AGM mould, along the way obtaining representation results for other existing revision operators in the literature, such as the Dalal operator and a recently introduced distance-based min-max operator.