  We prove completeness of preferential conditional logic with respect to
convexity over finite sets of points in the Euclidean plane. A conditional is
defined to be true in a finite set of points if all extreme points of the set
interpreting the antecedent satisfy the consequent. Equivalently, a conditional
is true if the antecedent is contained in the convex hull of the points that
satisfy both the antecedent and consequent. Our result is then that every
consistent formula without nested conditionals is satisfiable in a model based
on a finite set of points in the plane. The proof relies on a result by Richter
and Rogers showing that every finite abstract convex geometry can be
represented by convex polygons in the plane.
