Natural revision is contingently-conditionalized revision
Paolo Liberatore
TL;DR
This work analyzes natural revision, showing its limitations under counterexamples and then extends the framework to conditional beliefs. It derives that natural revision on a conditional $P>A$ operates within a contingent context, captured by $P \leq \min(PA)$, and contrasts it with uncontingent and lexicographic revisions grounded in the principle of naivety and minimal change. The paper formalizes the definitions, proves minimal-change properties, and discusses how different principle choices (naivety vs indifference) shape the resulting revision operators. It situates natural revision among related approaches (Boutilier–Goldszmidt, Nayak, Hansson, Chandler–Booth, Kern-Isberner) and explores extensions such as system-Z and line-down lexicographic variants. The results illuminate when natural revision is appropriate and how to navigate conditional belief revision in practice, with open questions about broader applicability and integration with other formalisms.
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.