Explaining Updates by Minimal Sums

Human reasoning about developments of the world involves always an assumption 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, (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 relation ≺dist. We show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions. Our main result is a general representation theorem in the spirit of Kraus, Lehmann and Magidor.