# Contextuality, Cohomology and Paradox

arXiv: https://arxiv.org/abs/1502.03097 · HTML: https://mlsanity.com/paper/1502.03097/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2015.

## Built on by (most cited first, 4 of 4)

- [On the Quantum-like Contextuality of Ambiguous Phrases](https://mlsanity.com/paper/2107.14589/) (2021)
- [On the Sheafification of Higher-Order Message Passing](https://mlsanity.com/paper/2509.23020/) (2025)
- [PHEATPRUNER: Interpretable Data-centric Feature Selection for Multivariate Time Series Classification through Persistent Homology](https://mlsanity.com/paper/2504.18329/) (2025)
- [Capability Sheaves for Compositional Agent-Harness Repair: Controlled Quotients and a Real-Repository Stress Test](https://mlsanity.com/paper/2608.13228/) (2026)

## Abstract (arXiv)

Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.