Credibility-Limited Revision for Epistemic Spaces
Kai Sauerwald
TL;DR
The paper addresses belief revision in unrestricted epistemic spaces, where inconsistent beliefs are permitted, by showing that standard credibility-limited revision cannot accommodate AGM revisions. It introduces extended credibility-limited revision as an axiomatic extension that replaces a restrictive postulate with two weaker ones and provides a semantic characterization via faithful credibility-limited assignments. The main results prove that all AGM revision operators are included in the extended class and that the extended framework generalizes CLR while remaining compatible with inconsistent epistemic states. This yields a unified, formally tractable approach to iterated belief change in richly expressive epistemic spaces, with potential relevance to cognitive logics and descriptional theories. The work also clarifies the relationship between AGM, CLR, and extended CLR in the unrestricted setting and offers avenues for comparing alternative extensions in the literature.
Abstract
We consider credibility-limited revision in the framework of belief change for epistemic spaces, permitting inconsistent belief sets and inconsistent beliefs. In this unrestricted setting, the class of credibility-limited revision operators does not include any AGM revision operators. We extend the class of credibility-limited revision operators in a way that all AGM revision operators are included while keeping the original spirit of credibility-limited revision. Extended credibility-limited revision operators are defined axiomatically. A semantic characterization of extended credibility-limited revision operators that employ total preorders on possible worlds is presented.