Topos-Based Logic for Quantum Systems and Bi-Heyting Algebras

TL;DR

This paper introduces a topos-based logical framework for quantum systems, associating each with a complete bi-Heyting algebra that models contextual propositions about physical quantities.

Contribution

It develops a novel topos-theoretic approach linking quantum systems to bi-Heyting algebras, providing a new logical structure for quantum contextuality.

Findings

Associates quantum systems with complete bi-Heyting algebras

Models contextual propositions about quantum physical quantities

Provides a logical framework for quantum contextuality

Abstract

To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of the quantum system.