Natural revision is contingently-conditionalized revision

TL;DR

This paper extends natural belief revision to handle conditionals, showing it restricts belief changes to current conditions and clarifies when it is appropriate to do so.

Contribution

It introduces an extension of natural revision from simple truths to conditionals, based on minimal change and naivety principles.

Findings

Natural revision restricts belief changes to current conditions.

The extension clarifies when natural revision is appropriate.

Comparison with unrestricting revision highlights current conditions.

Abstract

Natural revision seems so natural: it changes beliefs as little as possible to incorporate new information. Yet, some counterexamples show it wrong. It is so conservative that it never fully believes. It only believes in the current conditions. This is right in some cases and wrong in others. Which is which? The answer requires extending natural revision from simple formulae expressing universal truths (something holds) to conditionals expressing conditional truth (something holds in certain conditions). The extension is based on the basic principles natural revision follows, identified as minimal change and naivety: change mind as little as possible; believe what not contradicted. The extension says that natural revision restricts changes to the current conditions. A comparison with an unrestricting revision shows what exactly the current conditions are. It is not what currently considered true if it contradicts the new information. It includes something more and more unlikely until the new information is at least possible.