  In this work we present a generalization of the recently developed Hardy-like
logical proof of contextuality and of the so-called KCBS contextuality
inequality for any qudit of dimension greater than three. Our approach uses
compatibility graphs that can only be satisfied by qudits. We find a
construction for states and measurements that satisfy these graphs and
demonstrate both logical and inequality based contextuality for qudits.
Interestingly, the quantum violation of the inequality is constant as dimension
increases. We also discuss the issue of imprecision in experimental
implementations of contextuality tests and a way of addressing this problem
using the notion of ontological faithfulness.
