  This paper provides a systematic yet accessible presentation of the
Contextuality-by-Default theory. The consideration is confined to finite
systems of categorical random variables, which allows us to focus on the basics
of the theory without using full-scale measure-theoretic language.
Contextuality-by-Default is a theory of random variables identified by their
contents and their contexts, so that two variables have a joint distribution if
and only if they share a context. Intuitively, the content of a random variable
is the entity the random variable measures or responds to, while the context is
formed by the conditions under which these measurements or responses are
obtained. A system of random variables consists of stochastically unrelated
"bunches," each of which is a set of jointly distributed random variables
sharing a context. The variables that have the same content in different
contexts form "connections" between the bunches. A probabilistic coupling of
this system is a set of random variables obtained by imposing a joint
distribution on the stochastically unrelated bunches. A system is considered
noncontextual or contextual according to whether it can or cannot be coupled so
that the joint distributions imposed on its connections possess a certain
property (in the present version of the theory, "maximality"). We present a
criterion of contextuality for a special class of systems of random variables,
called cyclic systems. We also introduce a general measure of contextuality
that makes use of (quasi-)couplings whose distributions may involve negative
numbers or numbers greater than 1 in place of probabilities.
