Gaerdenfors' Postulates

Publication	Gaerdenfors/88a: Knowledge in Flux --- Modeling the Dynamics of Epistemic States
Name	Gaerdenfors' Postulates
Description	Gaerdenfors has set up six postulates, every revision operator shall fulfill. Let Cn(S) denote the set of formulas implied by S: Cn(S) := { f | S ⊨ f }, Cn(∅) denotes the set of all tautologies. B denote a closed theory, where closed means B = Cn(B), F (and G) denote a set of facts, rev(B, F) denote a revision of theory B, that does not imply any fact f ∈ F. Then Gaerdenfors' postulates are: Closure: rev(B, F) shall be a closed theory, again. Inclusion: The revised theory shall be a subset of the former theory. rev(B, F) ⊆ B Vacuity: If the theory does not contain any fact in F, the revision operator shall not change the theory. If F ∩ B = ∅, then rev(B, F) = B. Success: If F does not contain a tautology, then a revised theory should not contain any fact in F (anymore). If F ∩ Cn(∅) = ∅, then F ∩ rev(B, F) = ∅. Preservation: Two sets of facts, having the same consequences, should lead to the same revision of a theory. If Cn(F) = Cn(G), then rev(B, F) = rev(B, G). Recovery: A revision of a theory should have the property, that adding the facts of the set F after a revision step by F, results in the former theory, or in a superset of the former theory. B ⊆ Cn( rev(B, F) ∪ F ).
Dm Step	Revision