System of Spheres-based Two Level Credibility-limited Revisions

TL;DR

This paper introduces a new approach to belief revision using a two-level credibility system, employing Grove's systems of spheres to formalize and characterize the revision process.

Contribution

It proposes a construction for two-level credibility-limited revision operators based on Grove's systems of spheres and provides an axiomatic characterization.

Findings

The operators behave as standard revision at the highest credibility level.

At the second level, revision coincides with contraction by negation.

If the sentence is not credible, belief set remains unchanged.

Abstract

Two level credibility-limited revision is a non-prioritized revision operation. When revising by a two level credibility-limited revision, two levels of credibility and one level of incredibility are considered. When revising by a sentence at the highest level of credibility, the operator behaves as a standard revision, if the sentence is at the second level of credibility, then the outcome of the revision process coincides with a standard contraction by the negation of that sentence. If the sentence is not credible, then the original belief set remains unchanged. In this paper, we propose a construction for two level credibility-limited revision operators based on Grove's systems of spheres and present an axiomatic characterization for these operators.