Explaining Updates by minimal sums

Abstract

Human reasoning about developments of the world involves always an assumption of \emph{inertia}. We discuss two approaches for formalizing such an assumption, based on the concept of an \emph{explanation}: \emph{(1)} there is a general preference relation given on the set of all explanations, \emph{(2)} there is a notion of a \emph{distance} between models and explanations are \emph{preferred} if their sum of distances is minimal. 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. Also cross-referenced as UMIACS-TR-99-47