Editing Belief revision (section)

==The Ramsey test<!--[[Ramsey test]], [[Ramsey Test]], [[Ramsey's test]], [[Ramsey's Test]] redirect here-->==
The evaluation of a [[counterfactual conditional]] <math>a > b</math> can be done, according to the '''Ramsey test'''<!--boldface per WP:R#PLA--> (named for [[Frank P. Ramsey]]), to the hypothetical addition of <math>a</math> to the set of current beliefs followed by a check for the truth of <math>b</math>. If <math>K</math> is the set of beliefs currently held, the Ramsey test is formalized by the following correspondence:

: <math>a > b \in K</math> if and only if <math>b \in K * a</math>

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 <math>></math>, the Ramsey test leads to the Gärdenfors 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 <math>a>b</math> can be present in belief sets and revising formulae. Several solutions to this problem have been proposed.