Optimal Belief Revision

TL;DR

This paper introduces an optimal belief revision method that minimizes effort by focusing on specific informational goals, using formal contexts and accessibility orderings to efficiently update knowledge bases.

Contribution

It presents a novel formal framework for belief revision based on optimal contexts and accessibility, improving the efficiency of belief updates.

Findings

Formal description of contexts as sub-theories with parameters

Method to construct contexts for belief revision

Characterization of accessibility rankings for knowledge bases

Abstract

We propose a new approach to belief revision that provides a way to change knowledge bases with a minimum of effort. We call this way of revising belief states optimal belief revision. Our revision method gives special attention to the fact that most belief revision processes are directed to a specific informational objective. This approach to belief change is founded on notions such as optimal context and accessibility. For the sentential model of belief states we provide both a formal description of contexts as sub-theories determined by three parameters and a method to construct contexts. Next, we introduce an accessibility ordering for belief sets, which we then use for selecting the best (optimal) contexts with respect to the processing effort involved in the revision. Then, for finitely axiomatizable knowledge bases, we characterize a finite accessibility ranking from which the accessibility ordering for the entire base is generated and show how to determine the ranking of an arbitrary sentence in the language. Finally, we define the adjustment of the accessibility ranking of a revised base of a belief set.