Belief revision and 3-valued logics: Characterization of 19,683 belief change operators

TL;DR

This paper introduces a 3-valued logic framework for belief revision, generalizing total preorders to three levels, and provides syntactical characterizations of belief change operators within this setting.

Contribution

It extends classical belief revision models by incorporating a three-valued logic and characterizes a large set of belief change operators in this new framework.

Findings

Introduces a 3-valued logic for belief revision.

Provides syntactical characterizations of belief change operators.

Analyzes the structure of belief change in the three-valued setting.

Abstract

In most classical models of belief change, epistemic states are represented by theories (AGM) or formulas (Katsuno-Mendelzon) and the new pieces of information by formulas. The Representation Theorem for revision operators says that operators are represented by total preorders. This important representation is exploited by Darwiche and Pearl to shift the notion of epistemic state to a more abstract one, where the paradigm of epistemic state is indeed that of a total preorder over interpretations. In this work, we introduce a 3-valued logic where the formulas can be identified with a generalisation of total preorders of three levels: a ranking function mapping interpretations into the truth values. Then we analyse some sort of changes in this kind of structures and give syntactical characterizations of them.