Tuesday, 9 November 2004
On the Gärdenfors Impossibility Theorem
Neil Tennant
Ohio State University
12:05 pm, 817R Cathedral of Learning

Abstract: In 1986 Peter Gärdenfors published a theorem which has been widely interpreted as showing that it is impossible to adjoin to the AGM-postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So Gärdenfors’s result has been interpreted as demonstrating that it is impossible to combine the Ramsey test with the AGM-postulates.

I show that this interpretation of Gärdenfors’s result is unwarranted. His formal statement of the principle of monotonicity of revisions is too strong. Crucial applications of this principle in Gärdenfors’s proof require one to regard as revisions certain instances of theory-change that are really expansions.

If monotonicity is stated only for genuine revisions, then Gärdenfors’s proof does not go through. Nor can such a proof go through. For, when the monotonicity principle for revisions is correctly confined to revisions that are not expansions, one can establish a contrary consistency result. This requires only a slight adjustment to the AGM-postulates, in order to ensure that the three operations of expansion, contraction and revision trichotomize the domain of theory-changes.