Characterization of AGM Belief Contraction in Terms of Conditionals

TL;DR

This paper offers a semantic framework for understanding AGM belief contraction using frames with Kripke relations and selection functions, linking belief change to conditionals in a formal setting.

Contribution

It introduces a novel semantic characterization of AGM belief contraction through the use of frames involving Kripke relations and Stalnaker-Lewis selection functions.

Findings

Provides a formal semantic model for belief contraction

Connects belief contraction with conditionals at the semantic level

Enhances understanding of belief change mechanisms

Abstract

We provide a semantic characterization of AGM belief contraction based on frames consisting of a Kripke belief relation and a Stalnaker-Lewis selection function. The central idea is as follows. Let K be the initial belief set and K-A be the contraction of K by the formula A; then B belongs to the set K-A if and only if, at the actual state, the agent believes B and believes that if not-A is (were) the case then B is (would be) the case.