Explaining updates by minimal sums

Human reasoning about developments of the world involves always an assumpti on of inertia. We discuss two approaches for formalizing such an assumption , based on the concept of an explanation: (1) there is a general preference relation < given on the set of all explanations and (2) there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal. Each distance dist naturally induces a preference re lation < (dist), We show exactly under which conditions the converse is tru e as well and therefore both approaches are equivalent modulo these conditi ons. Our main result is a general representation theorem in the spirit of K i-aus, Lehmann and Magidor. (C) 2001 Elsevier Science B.V. All rights reser ved.