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Revision Sequences and Nested Conditionals

The truth conditions for conditional sentences have been well-studied, but few compelling attempts have been made to define means of evaluating iterated or nested conditionals. In particular, most approaches impose very few constraints on the set of conditionals an agent can hold after revision of its belief set. In this paper we describe the method of natural revision that ensures the preservation of conditional beliefs after revision by an objective belief. Our model, based on a simple modal logic for beliefs and conditionals, extends the AGM theory of belief revision to account for sentences of objective revisions of a belief set. This model of revision ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, natural revision provides truth conditions for arbitrary right-nested conditionals. We show that the problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals, indicating that iterated revision can be simulated by virtual updates. We also briefly describe certain reductions to (sometimes tractable) propositional inference, and other informational properties.