On Principles and Representations for Extended Contextuality (2410.05723v1)

Abstract: There has been recent interest in whether the concept of quantum contextuality can be extended to systems with disturbance or signaling while retaining the essential properties of standard contextuality. Dzhafarov and Kujala (arXiv:2302.11995) offer a provocative argument that the answer is always affirmative: If standard contextuality satisfies some principle that extended contextuality does not, then that principle must be non-substantive' in that it depends on a superficial choice of representation. Their argument is based on a`consistification'' procedure that maps all systems to nondisturbing ones and that preserves contextuality. This paper raises several objections to their argument, including that it neglects how substantive principles change their expression under a change of representation, that it begs the question by presuming the principles are based on non-substantive transformations, and that the argument applies universally to arbitrary extensions of contextuality.