On Contextuality as a Feature of Logic and Probability Theory

TL;DR

This paper explores how contextuality, a phenomenon where measurement outcomes depend on measurement settings, is a fundamental feature of probability theory and logic, not just quantum mechanics.

Contribution

It provides a mathematical framework showing that contextuality is inherent in probability and logic, extending beyond quantum physics.

Findings

Contextuality is a general feature of probability theory.

Mathematical formalism linking contextuality with logic.

Highlights the universality of contextuality beyond quantum mechanics.

Abstract

In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on which combination of observables was measured. This article gives a mathematical introduction to contextuality, emphasising its nature as a general feature of probability theory and logic, rather than of any particular quantum theory.