Belief revision,epistemic conditionals and the Ramsey test

Epistemic conditionals have often been thought to satisfy the Ramsey test (RT): If A, then B is acceptable in a belief state G if and only if B should be accepted upon revising G with A. But as Peter Gärdenfors has shown, RT conflicts with the intuitively plausible condition of Preservation on belief revision. We investigate what happens if (a) RT is retained while Preservation is weakened, or (b) vice versa. We also generalize Gärdenfors' approach by treating belief revision as a relation rather than as a function.In our semantic approach, the same relation is used to model belief revision and to give truth-conditions for conditionals. The approach validates a weak version of the Ramsey Test (WRR) — essentially, a restriction of RT to maximally consistent belief states.We prove that alternatives (a) and (b) are both consistent, but argue that (b) is philosophically more promising. Gärdenfors' belief-revision axioms are compatible with WRR together with RT from left to right: the only direction of the test that is defensible on intuitive grounds.An earlier version of this paper was presented at the conference on the dynamics of knowledge and belief at Lund University, 24–26 August 1989. We wish to thank Sven Danielsson, Peter Gärdenfors, Sören Halldén, David Makinson, Hugh Mellor, Michael Morreau, Nils-Eric Sahlin and Brian Skyrms for their very helpful suggestions and remarks. We are also grateful for thought-provoking criticism and comments from two anonymous referees.