Natural revision is contingently-conditionalized revision

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, indifference and naivety: change beliefs as little as possible; equate the likeliness of scenarios by default; believe all until 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

Revision by conditionals: from hook to arrow

Thebeliefrevisionliteraturehaslargelyfocussedontheissue of how to revise one’s beliefs in the light of information regardingmattersoffact.Hereweturntoanimportantbutcomparatively neglected issue: How might one extend a revision operatortohandleconditionalsasinput?Ourapproachtothis question of ‘conditional revision’ is distinctive insofar as it abstracts from the controversial details of how to revise by factual sentences. We introduce a ‘plug and play’ method for uniquelyextendinganyiteratedbeliefrevisionoperatortothe conditional case. The flexibility of our approach is achieved by having the result of a conditional revision by a Ramsey Test conditional (‘arrow’) determined by that of a plain revision by its corresponding material conditional (‘hook’). It is shown to satisfy a number of new constraints that are of independent interest