On Limited Non-Prioritised Belief Revision Operators with Dynamic Scope

TL;DR

This paper introduces dynamic-limited belief revision operators that revise beliefs based on a total preorder over a limited set of worlds, exploring their properties, iteration behavior, and applications to inherent beliefs.

Contribution

It formalizes dynamic-limited revision operators, characterizes their properties, and applies them to model belief revision involving inherent beliefs, providing a new framework in belief change theory.

Findings

Existence of dynamic-limited revision for certain belief sets.

Characterization of iteration postulates for these operators.

Representation theorem for inherence-limited revision operators.

Abstract

The research on non-prioritized revision studies revision operators which do not accept all new beliefs. In this paper, we contribute to this line of research by introducing the concept of dynamic-limited revision, which are revisions expressible by a total preorder over a limited set of worlds. For a belief change operator, we consider the scope, which consists of those beliefs which yield success of revision. We show that for each set satisfying single sentence closure and disjunction completeness there exists a dynamic-limited revision having the union of this set with the beliefs set as scope. We investigate iteration postulates for belief and scope dynamics and characterise them for dynamic-limited revision. As an application, we employ dynamic-limited revision to studying belief revision in the context of so-called inherent beliefs, which are beliefs globally accepted by the agent. This leads to revision operators which we call inherence-limited. We present a representation theorem for inherence-limited revision, and we compare these operators and dynamic-limited revision with the closely related credible-limited revision operators.