[Paper Review] Distance Semantics for Belief Revision

Karl Schlechta, Daniel Lehmann+1 more|arXiv (Cornell University)|Mar 17, 1996

Logic, Reasoning, and Knowledge20 references16 citations

TL;DR

This paper introduces distance semantics for belief revision by defining revision as selecting models of the new belief that are closest to the original belief set, using a distance metric between models. It extends the AGM postulates with new rationality constraints that govern iterated revisions, providing a formal framework for consistent and intuitive belief updates in dynamic environments.

ABSTRACT

A vast and interesting family of natural semantics for Belief Revision is defined. Suppose one is given a distance d between any two models. One may define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

Motivation & Objective

• To develop a formal semantics for belief revision based on model distances, enabling intuitive and rational belief updates.
• To extend the AGM postulates with new rationality postulates that govern the behavior of iterated belief revisions.
• To characterize a broad family of belief revision operations that are grounded in geometric proximity between models.
• To ensure consistency and rationality in belief change processes, especially when revisions are applied sequentially.

Proposed method

• Define a distance function d between any two models to measure their semantic similarity.
• Revise a belief theory K by a formula α using the set of models of α that are closest to the models of K, according to d.
• Formalize the revision operation as the theory corresponding to the closest models of α to K under d.
• Characterize the resulting revision family via a set of rationality postulates extending AGM, particularly for iterated revision.
• Use the distance-based selection to ensure that revisions preserve maximal consistency and minimal change.

Experimental results

Research questions

• RQ1 How can belief revision be formalized using a distance metric between models to ensure intuitive and rational updates?
• RQ2 What additional rationality postulates are needed to govern the behavior of iterated belief revisions beyond the AGM framework?
• RQ3 Can a unified semantics be defined that captures a broad family of rational belief revision operations through distance?
• RQ4 How does the distance-based approach ensure consistency across multiple revision steps?

Key findings

• The proposed distance semantics defines a natural and intuitive family of belief revision operations based on model proximity.
• The framework extends the AGM postulates with new rationality constraints that specifically address iterated revision behavior.
• The distance-based revision operation ensures minimal change by selecting models of the new belief that are closest to the original belief set.
• The approach provides a formal foundation for rational belief change that is both systematic and consistent across multiple revisions.