# Decrement Operators in Belief Change

## TL;DR

This paper introduces and analyzes decrement operators in belief change, providing a new framework for iterated contraction with formal postulates and representation theorems.

## Contribution

It presents a non-prioritized generalization of iterated contraction called weak decrement operators and explores their properties and subclasses.

## Key findings

- Defined decrement and weak decrement operators.
- Provided postulates and representation theorems for these operators.
- Identified two sub-types of decrement operators.

## Abstract

While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for each of them a representation theorem in the framework of total preorders is given. Furthermore, we present two sub-types of decrement operators.