Varieties of contextuality based on probability and structural nonembeddability

Abstract

Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas probabilistic contextuality still allows classical models, albeit with nonclassical probabilities, the logico-algebraic "strong" form of contextuality characterizes collections of quantum observables that have no faithfully embedding into (extended) Boolean algebras. Both forms indicate a classical in- or under-determination that can be termed "value indefinite" and formalized by partial functions of theoretical computer sciences.