# Kolmogorovian Censorship, Predictive Incompleteness, and the Locality Loophole in Bell Experiments

## TL;DR

The paper explores quantum probabilities through the lens of Kolmogorovian Censorship and predictive incompleteness, arguing for a framework that preserves locality while explaining Bell inequality violations.

## Contribution

The paper introduces predictive incompleteness as a novel framework for quantum probabilities that preserves relativistic locality.

## Key findings

- Kolmogorovian Censorship identifies classical probabilities within fixed measurement contexts but does not resolve conceptual tensions in Bell experiments.
- Predictive incompleteness offers a minimal framework matching experimental practice while preserving locality.
- The paper clarifies logical relations among quantum probability interpretations and justifies moving from Kolmogorov’s to Gleason’s framework.

## Abstract

We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness—the view that the quantum state is operationally incomplete until the measurement context is specified—provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov’s to Gleason’s framework for quantum probabilities.