On contextuality and logic in scientific discourse: Reply to Aliakbarzadeh, Kitto, and Bruza

TL;DR

This paper defends the Contextuality-by-Default (CbD) theory against recent criticisms, clarifying misunderstandings and showing its consistency and relation to traditional contextuality and ontic states.

Contribution

It refutes recent claims of contradiction in CbD, clarifies its specialization to consistent systems, and explains the role of ontic states within the theory.

Findings

The alleged contradiction in CbD is due to presentation issues.

CbD reduces to traditional contextuality in consistent systems.

Ontic states are either outside CbD's language or trivially reconstructed.

Abstract

Aliakbarzadeh, Kitto, and Bruza (arXiv:1909.13048v1) criticize the Contextuality-by-Default (CbD) theory in three ways: (1) they claim an internal contradiction within the theory, that consists in both denying and accepting the equality of stochastically unrelated random variables; (2) they find CbD deficient because when one confines one's attention to consistently connected systems (those with no disturbance/signaling) one can dispense with the double-indexation of random variables; and (3) they see no relationship between double-indexation and ontic states. This commentary shows that (re$\:$1) the contradiction is inserted in the presentation of CbD by the authors of the paper; (re$\:$2) in the case of consistently connected systems CbD properly specializes to traditional understanding of contextuality; and (re$\:$3) if ontic states are understood as quantum states, they are simply not within the language of CbD, and if they are understood as domain probability spaces for context-sharing random variables, they can be trivially reconstructed.