# Iterated Descriptor Revision and the Logic of Ramsey Test Conditionals

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## Abstract

Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a (set of) metalinguistic sentence(s) specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes (available belief sets) in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results that they generate in other systems. In addition to standard (sentential) Ramsey test conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning.

## Keywords

Descriptor revision Iterated revision Conditionals Darwiche-Pearl postulates Ramsey test Cumulative reasoning## Notes

### Acknowledgment

I would like to thank John Cantwell for a series of conversations on the logic of conditionals that were unusually helpful in the preparation of this paper.

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