A Qualified Kolmogorovian Account of Probabilistic Contextuality

Abstract

We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central principle (contextuality-by-default) is that the outputs indexed by mutually incompatible values of inputs are stochastically unrelated; but they can be coupled (imposed a joint distribution on) in a variety of ways. A system is characterized by a pattern of which outputs can be "directly influenced" by which inputs (a primitive relation, hypothetical or normative), and by certain constraints imposed on the outputs (such as Bell-type inequalities or their quantum analogues). The set of couplings compatible with these constraints determines the form of contextuality in the dependence of outputs on inputs. © 2014 Springer-Verlag Berlin Heidelberg.