Belief Revision - The Ramsey Test

The Ramsey Test

The evaluation of a counterfactual conditional can be done, according to the Ramsey test, to the hypothetical addition of to the set of current beliefs followed by a check for the truth of . If is the set of beliefs currently held, the Ramsey test is formalized by the following correspondence:

if and only if

If the considered language of the formulae representing beliefs is propositional, the Ramsey test gives a consistent definition for counterfactual conditionals in terms of a belief revision operator. However, if the language of formulae representing beliefs itself includes the counterfactual conditional connective, the Ramsey test leads to the Gardnefors triviality result: there is no non-trivial revision operator that satisfies both the AGM postulates for revision and the condition of the Ramsey test. This result holds in the assumption that counterfactual formulae like can be present in belief bases and revising formulae. Several solutions to this problem have been proposed.