Foundations of Quantum Contextual Topos: Integrating Modality and Topos Theory in Quantum Logic

2024/09/04 by Jesse Werbow, Werbow, Jesse
Computer Science · Physics and Astronomy · #03 #Advanced Algebra and Logic #Computability, Logic, AI Algorithms #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2409.12198

openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces the Quantum Contextual Topos (QCT), a novel framework that extends traditional quantum logic by embedding contextual elements within a topos-theoretic structure. This framework seeks to provide a classically-obedient tool for exploring the logical foundations of quantum mechanics. The QCT framework aims to address the limitations of classical quantum logic, particularly its challenges in capturing the dynamic and contextual nature of quantum phenomena. By integrating modal operators and classical propositional logic within a topos structure, the QCT offers a unified approach to modeling quantum systems. The main result of this work is demonstrating that the internal logic of QCT corresponds to a form of classical propositional polymodal logic. We do this by generalizing Stone's Representation Theorem for a specific case of polymodal algebras and their underlying Stone Spaces.

Related

• Quantum modal logic
• A Topos for Algebraic Quantum Theory
• The logical structure of contextuality and nonclassicality
• Throwing bridges: where and how can classical and quantum view be connected?
• Topos-Based Logic for Quantum Systems and Bi-Heyting Algebras